{"title":"Algebraic topology Books","description":"","products":[{"product_id":"operator-theory-by-example-oxford-graduate-texts-in-mathematics-9780192863874","title":"Operator Theory by Example Oxford Graduate Texts","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eAimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory, and covers twenty examples of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eThe text is supplemented by over 600 end-of-chapter exercises, designed to help the reader master the topics covered in the chapter, as well as providing an opportunity to further explore the vast operator theory literature. Each chapter also contains well researched historical facts which place each chapter within the broader context of the development of the field as a whole. * MathSciNet *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1: Hilbert Spaces 2: Diagonal Operators 3: Infinite Matrices 4: Two Multiplication Operators 5: The Unilateral Shift 6: The Cesàro Operator 7: The Volterra Operator 8: Multiplication Operators 9: The Dirichlet Shift 10: The Bergman Shift 11: The Fourier Transform 12: The Hilbert Transform 13: Bishop Operators 14: Operator Matrices 15: Constructions with the Shift Operator 16: Toeplitz Operators 17: Hankel Operators 18: Composition Operators 19: Subnormal Operators 20: The Compressed Shift","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732603646295,"sku":"9780192863874","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192863874.jpg?v=1791454085"},{"product_id":"more-concise-algebraic-topology-9780226511788","title":"More Concise Algebraic Topology","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eWith firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. This title addresses the course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. It covers topics that are useful for algebraic topologists.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\"All researchers in algebraic topology should have at least a passing acquaintance with the material treated in this book, much of which does not appear in any of the standard texts.\" (Kathryn Hess, Ecole Polytechnique Federale de Lausanne)\"","brand":"The University of Chicago Press","offers":[{"title":"Default Title","offer_id":48732910256471,"sku":"9780226511788","price":65.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780226511788.jpg?v=1719998914"},{"product_id":"differential-forms-in-algebraic-topology-9780387906133","title":"Differential Forms in Algebraic Topology","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eDeveloped from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e“Bott and Tu give us an introduction to algebraic  topology via differential forms, imbued with the spirit of a master who  knew differential forms way back when, yet written from a mature point  of view which draws together the separate paths traversed by de Rham  theory and homotopy theory. Indeed they assume \"an audience with prior  exposure to algebraic \u003cem\u003eor \u003c\/em\u003edifferential topology\". It would be  interesting to use Bott and Tu as the text for a first graduate course  in algebraic topology; it would certainly be a wonderful supplement to a  standard text. \u003cp\u003e“Bott and Tu write with a consistent  point of view and a style which is very readable, flowing smoothly from  topic to topic. Moreover, the differential forms and the general  homotopy theory are well integrated so that the whole is more than the  sum of its parts. \"Not intended to be foundational\", the book presents  most key ideas, at least in sketch form, from scratch, but does not  hesitate to quote as needed, without proof, major results of a technical  nature, e.g., Sard's Theorem, Whitney's Embedding Theorem and the Morse  Lemma on the form of a nondegenerate critical point.”\u003c\/p\u003e \u003cp\u003e—James D. Stasheff (Bulletin of the  American Mathematical Society)\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e“This book is an excellent  presentation of algebraic topology via differential forms. The first  chapter contains the de Rham theory, with stress on computability. Thus,  the Mayer-Vietoris technique plays an important role in the exposition.  The force of this technique is demonstrated by the fact that the  authors at the end of this chapter arrive at a really comprehensive  exposition of Poincaré duality, the Euler and Thom classes and the Thom  isomorphism.\u003c\/p\u003e \u003cp\u003e“The second chapter develops and  generalizes the Mayer-Vietoris technique to obtain in a very natural way  the Čech-de Rham complex and the Čech cohomology for presheaves. The  third chapter on spectral sequences is the most difficult one, but also  the richest one by the various applications and digressions into other  topics of algebraic topology: singular homology and cohomology with  integer coefficients and an important part of homotopy theory, including  the Hopf invariant, the Postnikov approximation, the Whitehead tower  and Serre’s theorem on the homotopy of spheres. The last chapter is  devoted to a brief and comprehensive description of the Chern and  Pontryagin classes.\u003c\/p\u003e \u003cp\u003e“A book which covers such an  interesting and important subject deserves some remarks on the style: On  the back cover one can read “With its stress on concreteness,  motivation, and readability, \u003cem\u003eDifferential forms in algebraic topology  \u003c\/em\u003eshould be suitable for self-study.” This must not be misunderstood  in the  ense that it is always easy to read the  book. The authors invite the reader to understand algebraic topology by  completing himself proofs and examples in the exercises. The reader who  seriously follows this invitation really learns a lot of algebraic  topology and mathematics in general.”\u003cbr\u003e \u003c\/p\u003e \u003cp\u003e—Hansklaus Rummler  (American Mathematical Society)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eI De Rham Theory.- II The ?ech-de Rham Complex.- III Spectral Sequences and Applications.- IV Characteristic Classes.- References.- List of Notations.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733726572887,"sku":"9780387906133","price":44.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387906133.jpg?v=1791378795"},{"product_id":"sheaves-in-geometry-and-logic-9780387977102","title":"Sheaves in Geometry and Logic","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eSheaves also appear in logic as carriers for models of set theory. Beginning with several examples, it explains the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\"A beautifully written book, a long and well motivated book packed with well chosen clearly explained examples. … authors have a rare gift for conveying an insider’s view of the subject from the start. This book is written in the best Mac Lane style, very clear and very well organized. … it gives very explicit descriptions of many advanced topics--you can learn a great deal from this book that, before it was published, you could only learn by knowing researchers in the field.\" (Wordtrade, 2008)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface; Prologue; Categorical Preliminaries; 1. Categories of Functors; 2. Sheaves of Sets; 3. Grothendieck Topologies and Sheaves; 4. First Properties of Elementary Topoi; 5. Basic Constructions of Topoi; 6. Topoi and Logic; 7. Geometric Morphisms; 8. Classifying Topoi; 9. Localic Topoi; 10. Geometric Logic and Classifying Topoi; Appendix: Sites for Topoi; Epilogue; Bibliography; Index of Notations; Index","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733727916375,"sku":"9780387977102","price":61.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387977102.jpg?v=1720001409"},{"product_id":"categories-for-the-working-mathematician-9780387984032","title":"Categories for the Working Mathematician","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003eFrom the reviews of the second edition:\u003c\/p\u003e\u003cp\u003e“The book under review is an introduction to the theory of categories which, as the title suggests, is addressed to the (no-nonsense) working mathematician, thus presenting the ideas and concepts of Category Theory in a broad context of mainstream examples (primarily from algebra). … the book remains an authoritative source on the foundations of the theory and an accessible first introduction to categories. … It is very well-written, with plenty of interesting discussions and stimulating exercises.” (Ittay Weiss, MAA Reviews, July, 2014)\u003c\/p\u003e\u003cp\u003eSecond Edition\u003c\/p\u003e\u003cp\u003e\u003ci\u003eS.M. Lane\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eCategories for the Working Mathematician\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003e\"A very useful introduction to category theory.\"—\u003c\/i\u003eINTERNATIONALE MATHEMATISCHE NACHRICHTEN\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1: Categories, Functors and Natural Transformation. 2: Constructions on Categories. 3: Universals and Limits. 4: Adjoints. 5: Limits. 6: Monads and Algebras. 7: Monoids. 8: Abelian Categories. 9: Special Limits. 10: Kan Extensions. 11: Symmetry and Braiding in Monoidal Categories. 12: Structures in Categories. Tables of Categories. Bibliography.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733728276823,"sku":"9780387984032","price":45.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387984032.jpg?v=1720001411"},{"product_id":"differential-geometry-in-the-large-9781108812818","title":"Differential Geometry in the Large","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe 2019 ''Australian-German Workshop on Differential Geometry in the Large'' represented an extraordinary cross section of topics across differential geometry, geometric analysis and differential topology. The two-week programme featured talks from prominent keynote speakers from across the globe, treating geometric evolution equations, structures on manifolds, non-negative curvature and Alexandrov geometry, and topics in differential topology. A joy to the expert and novice alike, this proceedings volume touches on topics as diverse as Ricci and mean curvature flow, geometric invariant theory, Alexandrov spaces, almost formality, prescribed Ricci curvature, and Kähler and Sasaki geometry.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'The high-quality surveys and original work in this book give a convenient path to understand some recent exciting developments in global Differential Geometry and Geometric Analysis. This should be of great value to graduate students entering the field, as well as to more experienced researchers looking for an updated perspective on a wide range of topics, ranging from nonnegative curvature and Alexandrov spaces to geometric flows and equivariant geometry.' Renato G. Bettiol, Lehman College, The City University of New York\u003cbr\u003e'The volume includes important additions to the literature including new results, new proofs of previous results, and simplified expositions, and also an excellent collection of surveys on recent activity. It is well written and offers a generous overview and invitation to a variety of modern, active topics in differential geometry.' Christopher Seaton, MAA Reviews\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction Owen Dearricott, Wilderich Tuschmann, Yuri Nikolayevsky, Thomas Leistner and Diarmuid Crowley; Part I. Geometric Evolution Equations and Curvature Flow: 1. Real geometric invariant theory Christoph Böhm and Ramiro A. Lafuente; 2. Convex ancient solutions to mean curvature flow Theodora Bourni, Mat Langford and Giuseppe Tinaglia; 3. Negatively curved three-manifolds, hyperbolic metrics, isometric embeddings in Minkowski space and the cross curvature flow Paul Bryan, Mohammad N. Ivaki and Julian Scheuer; 4. A mean curvature flow for conformally compact manifolds A. Rod Gover and Valentina-Mira Wheeler; 5. A survey on the Ricci flow on singular spaces Klaus Kröncke and Boris Vertman; Part II. Structures on Manifolds and Mathematical Physics: 6. Some open problems in Sasaki geometry Charles P. Boyer, Hongnian Huang, Eveline Legendre and Christina W. Tønnesen-Friedman; 7. The prescribed Ricci curvature problem for homogeneous metrics Timothy Buttsworth and Artem Pulemotov; 8. Singular Yamabe and Obata problems A. Rod Gover and Andrew K. Waldron; 9. Einstein metrics, harmonic forms and conformally Kähler geometry Claude LeBrun; 10. Construction of the supersymmetric path integral: a survey Matthias Ludewig; 11. Tight models of de-Rham algebras of highly connected manifolds Lorenz Schwachhöfer; Part III. Recent Developments in Non-Negative Sectional Curvature: 12. Fake lens spaces and non-negative sectional curvature Sebastian Goette, Martin Kerin and Krishnan Shankar; 13. Collapsed three-dimensional Alexandrov spaces: a brief survey Fernando Galaz-García, Luis Guijarro and Jesús Núñez-Zimbrón; 14. Pseudo-angle systems and the simplicial Gauss–Bonnet–Chern theorem Stephan Klaus; 15. Aspects and examples on quantitative stratification with lower curvature bounds Nan Li; 16. Universal covers of Ricci limit and RCD spaces Jiayin Pan and Guofang Wei; 17. Local and global homogeneity for manifolds of positive curvature Joseph A. Wolf.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738333917527,"sku":"9781108812818","price":53.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108812818.jpg?v=1791469742"},{"product_id":"intersection-homology-perverse-sheaves-with-applications-to-singularities-9783030276430","title":"Intersection Homology \u0026 Perverse Sheaves: with","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. \u003c\/p\u003eBeginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications.\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eIntersection Homology \u0026amp; Perverse Sheaves\u003c\/i\u003e is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e“This is quite a lot for a relatively short book! … this book provides a great jumping-off point for the reader who wants to learn about these tools by a route leading to the forefront of modern research via lots of concrete geometric examples.” (Greg Friedman, Mathematical Reviews, March, 2023)\u003c\/p\u003e\u003cp\u003e“This book is a welcome addition to the family of introductions to intersection cohomology and perverse sheaves. … the author takes care to introduce and motivate the main objects of study with geometric examples. There are also regular exercises which will help readers come to grips with the material. … this book will ... be a very useful resource … .” (Jon Woolf, zbMATH 1476.55001, 2022)\u003c\/p\u003e\u003cp\u003e“This is a good textbook to prepare a student to delve into the current literature, and also a good reference for a researcher. A mathematician whose research or interest has come in contact with these topics would also find this a stimulating read on the subject.” (MAA Reviews, April 7, 2020)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface.- 1. Topology of singular spaces: motivation, overview.- 2. Intersection Homology: definition, properties.- 3. L-classes of stratified spaces.- 4. Brief introduction to sheaf theory.- 5. Poincaré-Verdier Duality.- 6. Intersection homology after Deligne.- 7. Constructibility in algebraic geometry.- 8. Perverse sheaves.- 9. The Decomposition Package and Applications.- 10. Hypersurface singularities. Nearby and vanishing cycles.- 11. Overview of Saito's mixed Hodge modules, and immediate applications.- 12. Epilogue.- Bibliography.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743028654423,"sku":"9783030276430","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030276430.jpg?v=1791480469"},{"product_id":"algebraic-topology-9783030706074","title":"Algebraic Topology","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003e\u003ci\u003eAlgebraic Topology\u003c\/i\u003e is an introductory textbook based on a class for advanced high-school students at the Stanford University Mathematics Camp (SUMaC) that the authors have taught for many years. Each chapter, or lecture, corresponds to one day of class at SUMaC. The book begins with the preliminaries needed for the formal definition of a surface. Other topics covered in the book include the classification of surfaces, group theory, the fundamental group, and homology.\u003cbr\u003e \u003cbr\u003e This book assumes no background in abstract algebra or real analysis, and the material from those subjects is presented as needed in the text. This makes the book readable to undergraduates or high-school students who do not have the background typically assumed in an algebraic topology book or class. The book contains many examples and exercises, allowing it to be used for both self-study and for an introductory undergraduate topology course.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e“Algebraic topology provides a self-contained introduction to the field … . the book thus provides a particularly well-organized, interesting, and smooth exposition of its subject. … This particular book unique is that it provides a clear, elementary, but mathematically solid introduction to algebraic topology that keeps the subject interesting throughout. … provides a clear, readable, and detailed treatment of the ideas and proofs in the subject … .” (Thomas Mack, Mathematical Reviews, July, 2022)\u003c\/p\u003e“The book could easily be used in an undergraduate course or read by a bright high school student. It should certainly be in any high school library.” (Jonathan Hodgson, zbMATH 1481.55001, 2022)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction.- 1. Surface Preliminaries.- 2. Surfaces.- 3. The Euler Characteristic and Identification Spaces.- 4. Classification Theorem of Compact Surfaces.- 5. Introduction to Group Theory.- 6. Structure of Groups.- 7. Cosets, Normal Subgroups, and Quotient Groups.- 8. The Fundamental Group.- 9. Computing the Fundamental Group.- 10. Tools for Fundamental Groups.- 11. Applications of Fundamental Groups.- 12. The Seifert-Van Kampen Theorem.- 13. Introduction to Homology.- 14. The Mayer-Vietoris Sequence.- A. Topological Notions.- Bibliography.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743046414679,"sku":"9783030706074","price":31.34,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030706074.jpg?v=1720063874"},{"product_id":"homotopical-topology-9783319234878","title":"Homotopical Topology","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I. M. Gelfand. The first English translation, done many decades ago, remains very much in demand, although it has been long out-of-print and is difficult to obtain. Therefore, this updated English edition will be much welcomed by the mathematical community. Distinctive features of this book include: a concise but fully rigorous presentation, supplemented by a plethora of illustrations of a high technical and artistic caliber; a huge number of nontrivial examples and computations done in detail; a deeper and broader treatment of topics in comparison to most beginning books on algebraic topology; an extensive, and very concrete, treatment of the machinery of spectral sequences. The second edition contains an entirely new chapter on K-theory and the Riemann-Roch theorem (after Hirzebruch and Grothendieck).\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e“This book is a treasure trove for every mathematician who has to deal with classical algebraic topology and homotopy theory on the research level. … Its style is refreshing and informative, and the reader can feel the authors’ joy at sharing their insight into algebraic topology. … will be a useful addition to any mathematical bookshelf.” (Thomas Hüttemann, Mathematical Reviews, March, 2017)\u003c\/p\u003e\u003cp\u003e“This book covers all the basic material necessary for complete understanding of the fundamentals of algebraic topology … . This increase in the number of topics has made the book more convenient for serious students not only to extend their knowledge but also to gain insight into the interplay between these three subjects. … This book is designed to help students to select the level of learning subjects they want to reach … .” (Haruo Minami, zbMATH 1346.55001, 2016)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction.- Homotopy.- Homology.- Spectral Sequences of Fibrations.- Cohomology Operations.- The Adams Spectral Sequence.- K-Theory and Other Extraordinary Cohomology Theories.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743093043543,"sku":"9783319234878","price":47.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319234878.jpg?v=1791379134"},{"product_id":"cohomology-of-sheaves-9783540163893","title":"Cohomology of Sheaves","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis text exposes the basic features of cohomology of sheaves and its applications. The general theory of sheaves is very limited and no essential result is obtainable without turn­ ing to particular classes of topological spaces. The most satis­ factory general class is that of locally compact spaces and it is the study of such spaces which occupies the central part of this text. The fundamental concepts in the study of locally compact spaces is cohomology with compact support and a particular class of sheaves,the so-called soft sheaves. This class plays a double role as the basic vehicle for the internal theory and is the key to applications in analysis. The basic example of a soft sheaf is the sheaf of smooth functions on ~n or more generally on any smooth manifold. A rather large effort has been made to demon­ strate the relevance of sheaf theory in even the most elementary analysis. This process has been reversed in order to base the fundamental calculations in sheaf theory on elementary analysis.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eI. Homological Algebra.- 1. Exact categories.- 2. Homology of complexes.- 3. Additive categories.- 4. Homotopy theory of complexes.- 5. Abelian categories.- 6. Injective resolutions.- 7. Right derived functors.- 8. Composition products.- 9. Resume of the projective case.- 10. Complexes of free abelian groups.- 11. Sign rules.- II. Sheaf Theory.- 0. Direct limits of abelian groups.- 1. Presheaves and sheaves.- 2. Localization.- 3. Cohomology of sheaves.- 4. Direct and inverse image of sheaves. f*,f*.- 5. Continuous maps and cohomology!,.- 6. Locally closed subspaces, h!h.- 7. Cup products.- 8. Tensor product of sheaves.- 9. Local cohomology.- 10. Cross products.- 11. Flat sheaves.- 12. Hom(E,F).- III. Cohomology with Compact Support.- 1. Locally compact spaces.- 2. Soft sheaves.- 3. Soft sheaves on $$\\mathbb {R}$$n.- 4. The exponential sequence.- 5. Cohomology of direct limits.- 6. Proper base change and proper homotopy.- 7. Locally closed subspaces.- 8. Cohomology of the n-sphere.- 9. Dimension of locally compact spaces.- 10. Wilder’s finiteness theorem.- IV. Cohomology and Analysis.- 1. Homotopy invariance of sheaf cohomology.- 2. Locally compact spaces, countable at infinity.- 3. Complex logarithms.- 4. Complex curve integrals. The monodromy theorem.- 5. The inhomogenous Cauchy-Riemann equations.- 6. Existence theorems for analytic functions.- 7. De Rham theorem.- 8. Relative cohomology.- 9. Classification of locally constant sheaves.- V. Duality with Coefficient in a Field.- 1. Sheaves of linear forms.- 2. Verdier duality.- 3. Orientation of topological manifolds.- 4. Submanifolds of $$\\mathbb {R}$$n of codimension 1.- 5. Duality for a subspace.- 6. Alexander duality.- 7. Residue theorem for n-1 forms on $$\\mathbb {R}$$n.- VI. Poincare Duality with General Coefficients.- 1. Verdier duality.- 2. The dualizing complex D.- 3. Lefschetz duality.- 4. Algebraic duality.- 5. Universal coefficients.- 6. Alexander duality.- VII. Direct Image with Proper Support.- 1. The functor f!.- 2. The Künneth formula.- 3. Global form of Verdier duality.- 4. Covering spaces.- 5. Local form of Verdier duality.- VIII. Characteristic Classes.- 1. Local duality.- 2. Thom class.- 3. Oriented microbundles.- 4. Cohomology of real projective space.- 5. Stiefel-Whitney classes.- 6. Chern classes.- 7. Pontrjagin classes.- IX. Borel Moore Homology.- 1. Proper homotopy invariance.- 2. Restriction maps.- 3. Cap products.- 4. Poincare duality.- 5. Cross products and the Künneth formula.- 6. Diagonal class of an oriented manifold.- 7. Gysin maps.- 8. Lefschetz fixed point formula.- 9. Wu’s formula.- 10. Preservation of numbers.- 11. Trace maps in homology.- X. Application to Algebraic Geometry.- 1. Dimension of algebraic varieties.- 2. The cohomology class of a subvariety.- 3. Homology class of a subvariety.- 4. Intersection theory.- 5. Algebraic families of cycles.- 6. Algebraic cycles and Chern classes.- XI. Derived Categories.- 1. Categories of fractions.- 2. The derived category D (A).- 3. Triangles associated to an exact sequence.- 4. Yoneda extensions.- 5. Octahedra.- 6. Localization.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743129973079,"sku":"9783540163893","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783540163893.jpg?v=1791482025"},{"product_id":"basic-algebraic-topology-and-its-applications-9788132228417","title":"Basic Algebraic Topology and its Applications","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike.\u003cbr\u003eFocusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e“Adhikari’s work is an excellent resource for any individual seeking to learn more about algebraic topology. By no means will this text feel like an introduction to algebraic topology, but it does offer much for both beginners and experts. … the text will be a valuable reference on the bookshelf of any reader with an interest in algebraic topology. Summing Up: Recommended. Upper-division undergraduates and above; researchers and faculty.” (A. Misseldine, Choice, Vol. 54 (9), May, 2017)\u003c\/p\u003e\u003cp\u003e“I am pretty enthusiastic about this book. … it shows very good taste on the author’s part as far as what he’s chosen to do and how he’s chosen to do it. … Wow! What a nice book. I’m glad I have a copy.” (Michael Berg, MAA Reviews, maa.org, February, 2017)\u003c\/p\u003e“This is a comprehensive textbook on algebraic topology. … accessible to students of all levels of mathematics, so suitable for anyone wanting and needing to learn about algebraic topology. It can also offer a valuable resource for advanced students with a specialized knowledge in other areas who want to pursue their interest in this area. … further readings are provided at the end of each of them, which also enables students to study the subject discussed therein in more depth.” (Haruo Minami, zbMATH 1354.55001, 2017)\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003ePrerequisite Concepts and Notations.- Basic Homotopy.- The Fundamental Groups.-Covering Spaces.- Fibre Bundles, Vector Bundles and K-theory.- Geometry of Simplicial Complexes and Fundamental Groups.- Higher Homotopy Groups.- Products in Higher Homotopy Groups.- CW-complexes and Homotopy.- Eilenberg-MacLane Spaces.- Homology and Cohomology Theories.- Eilenberg-Steenrod Axioms for Homology and Cohomology Theories.- Consequences of the Eilenberg-Steenrod Axioms.- Some Applications of Homology Theory.- Spectral Homology and Cohomology Theories.- Obstruction Theory.- More Relations Between Homotopy and Homology Groups.- A Brief Historical Note.\u003c\/p\u003e","brand":"Springer, India, Private Ltd","offers":[{"title":"Default Title","offer_id":48743198622039,"sku":"9788132228417","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9788132228417.jpg?v=1720064544"},{"product_id":"lecture-notes-on-general-topology-9789811227417","title":"Lecture Notes On General Topology","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis book is intended as a one-semester course in general topology, a.k.a. point-set topology, for undergraduate students as well as first-year graduate students. Such a course is considered a prerequisite for further studying analysis, geometry, manifolds, and certainly, for a career of mathematical research. Researchers may find it helpful especially from the comprehensive indices.General topology resembles a language in modern mathematics. Because of this, the book is with a concentration on basic concepts in general topology, and the presentation is of a brief style, both concise and precise. Though it is hard to determine exactly which concepts therein are basic and which are not, the author makes efforts in the selection according to personal experience on the occurrence frequency of notions in advanced mathematics, and to related books that have received admirable reviews.This book also contains exercises for each chapter with selected solutions. Interrelationships among concepts are taken into account frequently. Twelve particular topological spaces are repeatedly exploited, which serve as examples to learn new concepts based on old ones.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface; Introduction; Topological Spaces; Continuous Maps and Homeomorphisms; Connectedness; Separation Axioms and Quotient Axioms; Compactness; Product Spaces and Quotient Spaces; Appendix: Some Elementary Inequalities;","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743277920599,"sku":"9789811227417","price":49.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811227417.jpg?v=1720064890"},{"product_id":"lectures-on-algebraic-topology-9789811232855","title":"Lectures On Algebraic Topology","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eAlgebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743279427927,"sku":"9789811232855","price":49.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811232855.jpg?v=1720064896"},{"product_id":"etale-cohomology-theory-revised-edition-9789814675086","title":"Etale Cohomology Theory (Revised Edition)","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eEtale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1\/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and ℓ-adic cohomology. The prerequisites for reading this book are basic algebraic geometry and advanced commutative algebra.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eDescent Theory; Etale Morphisms and Smooth Morphisms; Etale Fundamental Groups; Group Cohomology and Galois Cohomology; Etale Cohomology; Derived Categories and Derived Functors; Base Change Theorems; Duality; Finiteness Theorems;  -Adic Cohomology;","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743300268375,"sku":"9789814675086","price":180.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789814675086.jpg?v=1720064993"},{"product_id":"topological-differential-and-conformal-geometry-of-surfaces-9783030890315","title":"Topological, Differential and Conformal Geometry","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces.\u003c\/p\u003e  \u003cp\u003eBased on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e-1. Basic Differential Geometry.- 2. The Geometry of Manifolds.- 3. Hyperbolic Geometry.- 4. Some Examples and Sources of Geometry.- 5. Differential Topology of Surfaces.- 6. Riemann Surfaces.- 7. Surfaces of Genus \u003ci\u003eg\u003c\/i\u003e = 0.- 8. Surfaces with Riemannian Metric.- 9. Outline: Uniformization by Spectral Determinant.- 10. Uniformization by Energy.- 11. Families of Spaces.- 12. Functions on Riemann Surfaces.- 13. Line Bundles and Cohomology.- 14. Moduli Spaces and Teichmüller Spaces.- 15. Dimensions of Spaces of Holomorphic Sections.- 16. The Teichmüller Curve and its Universal Property.- 17. Riemann Surfaces and Algebraic Curves.- 18. The Jacobian of a Riemann Surface.- 19. Special Metrics on \u003ci\u003eJ\u003c\/i\u003e-Surfaces.- 20. The Fundamental Group and Coverings.- A. Reminder: Topology.- References.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48869362139479,"sku":"9783030890315","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030890315.jpg?v=1791480556"},{"product_id":"singularity-theory-and-its-application-9784931469327","title":"Singularity Theory And Its Application","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis is the proceedings of the meeting entitled “The 12th MSJ International Research Institute of the Mathematical Society of Japan 2003”. The papers cover several important topics in Singularity theory. Especially some of them are survey on motivic integrations, Thom polynomials, complex analytic singularity theory, generic differential geometry etc.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eInvariants of combinatorial line arrangements and Rybnikov's example by E. A. Bartolo, J. C. Ruber, J. I. Cogolludo-Agustin, and M. A. Marco-Buzunariz On time averaged optimization of dynamic inequalities on a circle by A. Davydov Thom polynomial computing strategies. A survey by L. M. Feher and R. Rimanyi The complex crystallographic groups and symmetries of $J_{10}$ by V. Goryunov and S. H. Man $tt^*$ geometry and mixed Hodge structures by C. Hertling Thom polynomials by M. Kazarian Quasi-convex decomposition in o-minimal structures. Application to the gradient conjecture by K. Kurdyka and A. Parusinski Homotopy groups of complements to ample divisors by A. Libgober Massey products of complex hypersurface complements by D. Matei On degree of mobility for complete metrics by V. S. Matveev Valuations and moduli of Goursat distributions by P. Mormul Semidifferentiabilite et version lisse de la conjecture de fibration de Whitney by C. Murolo and D. Trotman Submanifolds with a nondegenerate parallel normal vector field in euclidean spaces by J. J. Nuno-Ballesteros Weighted homogeneous polynomials and blow-analytic equivalence by O. M. Abderrahmane Characteristic classes of singular varieties by A. Parusinski On the classification of 7th degree real decomposable curves by G. M. Polotovskiy $\\mathcal A$-topological triviality of map germs and Newton filtrations by M. J. Saia and L. M. Soares On the topology of symmetry sets of smooth submanifolds in $\\mathbb{R}^k$ by V. D. Sedyh An infinitesimal criterion for topological triviality of families of sections of analytic varieties by M. A. S. Ruas and J. N. Tomazella Lines of principal curvature near singular end points of surfaces in $\\mathbb{R}^3$ by J. Sotomayor and R. Garcia $r$ does not imply $n$ or $(npf)$ for definable sets in non polynomially bounded o-minimal structures by D. Trotman and L. Wilson Valuations and local uniformization by M. Vaquie Arc spaces, motivic integration and stringy invariants by W. Veys Finite Dehn surgery along A'Campo's divide knots by Y. Yamada.","brand":"Mathematical Society of Japan","offers":[{"title":"Default Title","offer_id":48889419956567,"sku":"9784931469327","price":84.6,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9784931469327.jpg?v=1722554298"},{"product_id":"finsler-geometry-sapporo-2005-in-memory-of-makoto-matsumoto-9784931469426","title":"Finsler Geometry, Sapporo 2005 -- In Memory Of","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe volume contains surveys and original articles based on the talks given at the 40-th Finsler Symposium on Finsler Geometry held in the period September 9-10, 2005 at Hokkaido Tokai University, Sapporo, Japan. The Symposium's purpose was not only a meeting of the Finsler geometers from Japan and abroad, but also to commemorate the memory of the late Professor Makoto Matsumoto. The papers included in this volume contain fundamental topics of modern Riemann-Finsler geometry, interesting not only for specialists in Finsler geometry, but for researchers in Riemannian geometry or other fields of differential geometry and its applications also.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePart I. Professor Makoto Matsumoto: Photos of Makoto Matsumoto Matsumoto's legacy. The life and work of Professor Makoto Matsumoto by H. Shimada and S. V. Sabau Part II. Hunting Unicorns and Other Topics of Global Finsler Geometry: On two curvature-driven problems in Riemann-Finsler geometry by D. Bao Curvature properties of $(\\alpha, \\beta)$-metrics by S. Bacso, X. Cheng, and Z. Shen A connectedness principle in positively curved Finsler manifolds by I. R. Peter Riemann-Finsler surfaces by S. V. Sabau and H. Shimada Finsler geometry in the tangent bundle by L. Tamassy Part III. Finslerian Inspired Differential Geometry: Perturbations of constant connection Wagner spaces by P. L. Antonelli and S. F. Rutz Path geometries and almost Grassmann structures by M. Crampin and D. J. Saunders Ehresmann connections, metrics and good metric derivatives by R. L. Lovas, J. Pek, and J. Szilasi Dynamical systems of the Lagrangian and Hamiltonian mechanical systems by R. Miron Part IV. Complex Finsler Geometry: The Chern-Finsler connection and Finsler-Kahler manifolds by T. Aikou A survey of complex Finsler geometry by P.-M. Wong.","brand":"Mathematical Society of Japan","offers":[{"title":"Default Title","offer_id":48889420317015,"sku":"9784931469426","price":56.05,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9784931469426.jpg?v=1791482576"},{"product_id":"collected-works-of-anatole-katok-the-volume-i-9789811237751","title":"Collected Works of Anatole Katok The Volume I","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"World Scientific Publishing Company","offers":[{"title":"Default Title","offer_id":48890176373079,"sku":"9789811237751","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"collected-works-of-anatole-katok-the-volume-ii-9789811237775","title":"Collected Works of Anatole Katok The Volume II","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"World Scientific Publishing Company","offers":[{"title":"Default Title","offer_id":48890176700759,"sku":"9789811237775","price":297.0,"currency_code":"GBP","in_stock":true}]},{"product_id":"physical-and-numerical-models-in-knot-theory-including-applications-to-the-life-sciences-9789812561879","title":"Physical And Numerical Models In Knot Theory:","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and breadth of application are now widely appreciated and valuable progress continues to be made each year.This volume presents several contributions from researchers using computers to study problems that would otherwise be intractable. While computations have long been used to analyze problems, formulate conjectures, and search for special structures in knot theory, increased computational power has made them a staple in many facets of the field. The volume also includes contributions concentrating on models researchers use to understand knotting, linking, and entanglement in physical and biological systems. Topics include properties of knot invariants, knot tabulation, studies of hyperbolic structures, knot energies, the exploration of spaces of knots, knotted umbilical cords, studies of knots in DNA and proteins, and the structure of tight knots. Together, the chapters explore four major themes: physical knot theory, knot theory in the life sciences, computational knot theory, and geometric knot theory.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePhysical Knot Theory: Universal Energy Spectrum of Tight Knots and Links in Physics (R Buniy \u0026amp; T Kephart); Three Knotty Ideas in Geometry: Pearl-Number, Ropelength and Rope Packing (R Kusner \u0026amp; W Kusner); A Tutorial on Knot Energies (E J J van Rensburg); Knot Theory in the Life Sciences: Folding Complexity in a Random-Walk Copolymer Model (G Arteca); Protein Folds, Knots and Tangles (W Taylor); Monte Carlo Simulations of Gel-Electrophoresis of DNA Knots (C Weber et al.); Computational Knot Theory: Ropelength of Tight Polygonal Knots (J Baranska et al.); Topological Entropic Force Between a Pair of Random Knots Forming a Fixed Link (T Deguchi); Universal Characteristics of Polygonal Knot Probabilities (K Millett \u0026amp; E Rawdon); Geometric Knot Theory: Quadrisecants of Knots with Small Crossing Number (G T Jin); Minimal Flat Knotted Ribbons (L Kauffman); Conjectures on the Enumeration of Alternating Links (P Zinn-Justin); and other papers.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48890199802199,"sku":"9789812561879","price":172.8,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789812561879.jpg?v=1791484022"},{"product_id":"stochastic-analysis-on-manifolds-9780821808023","title":"Stochastic Analysis on Manifolds","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eProbability theory has become a convenient language and a useful tool in many areas of modern analysis. This book intends to explore part of this connection concerning the relations between Brownian motion on a manifold and analytical aspects of differential geometry. It begins with a review of stochastic differential equations on Euclidean space.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction Stochastic differential equations and diffusions Basic stochastic differential geometry Brownian motion on manifolds Brownian motion and heat kernel Short-time asymptotics Further applications Brownian motion and analytic index theorems Analysis on path spaces Notes and comments General notations Bibliography Index.","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":49083682947415,"sku":"9780821808023","price":73.8,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780821808023.jpg?v=1725549706"},{"product_id":"holomorphic-foliations-with-singularities-key-concepts-and-modern-results-9783030767044","title":"Holomorphic Foliations with Singularities: Key","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis concise textbook gathers together key concepts and modern results on the theory of holomorphic foliations with singularities, offering a compelling vision on how the notion of foliation, usually linked to real functions and manifolds, can have an important role in the holomorphic world, as shown by modern results from mathematicians as H. Cartan, K. Oka, T. Nishino, and M. Suzuki.\u003cbr\u003eThe text starts with a gentle presentation of the classical notion of foliations, advancing to holomorphic foliations and then holomorphic foliations with singularities. The theory behind reduction of singularities is described in detail, as well the cases for dynamics of a local diffeomorphism and foliations on complex projective spaces. A final chapter brings recent questions in the field, as holomorphic flows on Stein spaces and transversely homogeneous holomorphic foliations, along with a list of open questions for further study and research. Selected exercises at the end of each chapter help the reader to grasp the theory.\u003cbr\u003eGraduate students in Mathematics with a special interest in the theory of foliations will especially benefit from this book, which can be used as supplementary reading in Singularity Theory courses, and as a resource for independent study on this vibrant field of research.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface.- The Classical Notions of Foliations.- Some Results from Several Complex Variables.- Holomorphic Foliations: Nonsingular Case.- Holomorphic Foliations with Singularities.- Holomorphic Foliations Given by Closed 1-Forms.- Reduction of Singularities.- Holomorphic First Integrals.- Dynamics of a Local Diffeomorphism.- Foliations on Complex Projective Spaces.- Foliations with Algebraic Limit Sets.- Some Modern Questions.- Miscellaneous exercises and some open questions.\u003cbr\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49372688875863,"sku":"9783030767044","price":53.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030767044.jpg?v=1791480531"},{"product_id":"braid-groups-9780387338415","title":"Braid Groups","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eIn this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence;\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\"Details on … braid groups are carefully provided by Kassel and Turaev’s text Braid Groups. … Braid Groups is very well written. The proofs are detailed, clear, and complete. ... The text is to be praised for its level of detail. … For people … who want to understand current research in braid group related areas, Braid Groups is an excellent, in fact indispensable, text.\" (Scott Taylor, The Mathematical Association of America, October, 2008)\u003c\/p\u003e\u003cp\u003e\"This is a very useful, carefully written book that will bring the reader up to date with some of the recent important advances in the study of the braid groups and their generalizations. It continues the tradition of these high quality graduate texts in mathematics. The book could easily be used as a text for a year course on braid groups for graduate students, one advantage being that the chapters are largely independent of each other.\" (Stephen P. Humphries, Mathematical Reviews, Issue 2009 e)\u003c\/p\u003e\u003cp\u003e“This book is a comprehensive introduction to the theory of braid groups. Assuming only a basic knowledge of topology and algebra, it is intended mainly for graduate and postdoctoral students.” (Hirokazu Nishimura, Zentralblatt MATH, Vol. 1208, 2011)\u003c\/p\u003e\u003cp\u003e“The book of Kassel and Turaev is a textbook … for graduate students and researchers. As such, it covers the basic material on braids, knots, and links … at a level which requires minimal background, yet moves rapidly to non-trivial topics. … It is a carefully planned and well-written book; the authors are true experts, and it fills a gap. … it will have many readers.” (Joan S. Birman, Bulletin of the American Mathematical Society, Vol. 48 (1), January, 2011)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eBraids and Braid Groups.- Braids, Knots, and Links.- Homological Representations of the Braid Groups.- Symmetric Groups and Iwahori#x2013;Hecke Algebras.- Representations of the Iwahori#x2013;Hecke Algebras.- Garside Monoids and Braid Monoids.- An Order on the Braid Groups.- Presentations of SL(Z) and PSL(Z).- Fibrations and Homotopy Sequences.- The Birman#x2013;Murakami#x2013;Wenzl Algebras.- Left Self-Distributive Sets.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":49401969639767,"sku":"9780387338415","price":71.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387338415.jpg?v=1791459029"},{"product_id":"gateaux-differentiability-of-convex-functions-and-topology-9780471168225","title":"Gâteaux Differentiability of Convex Functions and","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis text puts together folklore results touching weak Asplund spaces. It presents a thorough examination of weak Asplund cases. Nonseparable Banach spaces, renorming, and differentiability are stressed throughout the text and all subclasses, including inferences and counterexamples are discussed. It also covers Stegall''s classes, fragmentability, and long sequences of linear projections. Notes, remarks and questions end each chapter.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eCanonical Examples of Weak Asplund Spaces.\u003cbr\u003e \u003cbr\u003e Properties of Gateaux Differentiability Spaces and Weak AsplundSpaces.\u003cbr\u003e \u003cbr\u003e Stegall's Classes.\u003cbr\u003e \u003cbr\u003e Two More Concrete Classes of Banach Spaces that Lie in .\u003cbr\u003e \u003cbr\u003e Fragmentability.\u003cbr\u003e \u003cbr\u003e \"Long Sequences\" of Linear Projections.\u003cbr\u003e \u003cbr\u003e Vaak Spaces and Gul'ko Compacta.\u003cbr\u003e \u003cbr\u003e A Characterization of WCG Spaces and of Eberlein Compacta.\u003cbr\u003e \u003cbr\u003e Main Open Questions and Problems.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e Index.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402507198807,"sku":"9780471168225","price":136.76,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471168225.jpg?v=1730480612"},{"product_id":"functional-analysis-an-introduction-to-banach-space-theory-43-pure-and-applied-mathematics-a-wiley-series-of-texts-monographs-and-tracts-9780471372141","title":"Functional Analysis An Introduction to Banach","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eA powerful introduction to one of the most active areas of theoretical and applied mathematics  This distinctive introduction to one of the most far-reaching and beautiful areas of mathematics focuses on Banach spaces as the milieu in which most of the fundamental concepts are presented.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\"This textbook for a two-semester course in functional analysis presents the basic ideas, techniques, and methods that form the underpinnings of the discipline.\" (SciTech Book News, Vol. 25, No. 3, September 2001)\u003cbr\u003e \u003cbr\u003e \"...a useful book which helps the student to understand Banach space theory.\" (Mathematical Reviews, 2003a)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface.\u003cbr\u003e \u003cbr\u003e Introduction.\u003cbr\u003e \u003cbr\u003e Basic Definitions and Examples.\u003cbr\u003e \u003cbr\u003e Basic Principles with Applications.\u003cbr\u003e \u003cbr\u003e Weak Topologies and Applications.\u003cbr\u003e \u003cbr\u003e Operators on Banach Spaces.\u003cbr\u003e \u003cbr\u003e Bases in Banach Spaces.\u003cbr\u003e \u003cbr\u003e Sequences, Series, and a Little Geometry in Banach Spaces.\u003cbr\u003e \u003cbr\u003e Bibliography.\u003cbr\u003e \u003cbr\u003e Author\/Name Index.\u003cbr\u003e \u003cbr\u003e Subject Index\u003cbr\u003e \u003cbr\u003e Symbol Index.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402577125719,"sku":"9780471372141","price":155.66,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471372141.jpg?v=1730480820"},{"product_id":"shape-and-shape-theory-wiley-series-in-probability-and-statistics-9780471968238","title":"Shape and Shape Theory Wiley Series in","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003ePioneered by David Kendall, the statistical theory of shape is an emerging area generating considerable interest for statisticians, engineers, and computer scientists. Co--written by Dr. Kendall, this volume presents a coherent theory of shape developed from Kendalla s own approach known as static and kinematic theory.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\"This is a fascinating book mixing geometry, topology and probability theory...\" (\u003ci\u003eLondon Mathematical Society Bulletin\u003c\/i\u003e, Vol 32, 2000)  \u003cp\u003e\"The potential value that his volume should have to researchers in many areas for years to come.\" (\u003ci\u003eShort Book Reviews\u003c\/i\u003e, August 2000)\u003c\/p\u003e \u003cp\u003e\"I would like to conclude this review by strongly recommending that geodists have this book on desk within ready reach of hands\" (\u003ci\u003eJournal of Geodesy\u003c\/i\u003e, Vol. 75, 2001)\u003c\/p\u003e \u003cp\u003e\"...a mathematical jewel...\" (\u003ci\u003eMathematical Reviews\u003c\/i\u003e, 2003g)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eShapes and Shape Spaces.\u003cbr\u003e \u003cbr\u003e The Global Structure of Shape Spaces.\u003cbr\u003e \u003cbr\u003e Computing the Homology of Cell Complexes.\u003cbr\u003e \u003cbr\u003e A Chain Complex for Shape Spaces.\u003cbr\u003e \u003cbr\u003e The Homology Groups of Shape Spaces.\u003cbr\u003e \u003cbr\u003e Geodesics in Shape Spaces.\u003cbr\u003e \u003cbr\u003e The Riemannian Structure of Shape Spaces.\u003cbr\u003e \u003cbr\u003e Induced Shape-Measures.\u003cbr\u003e \u003cbr\u003e Mean Shapes and the Shape of the Means.\u003cbr\u003e \u003cbr\u003e Visualising the Higher Dimensional Shape Spaces.\u003cbr\u003e \u003cbr\u003e General Shape Spaces.\u003cbr\u003e \u003cbr\u003e Appendix.\u003cbr\u003e \u003cbr\u003e Bibliography.\u003cbr\u003e \u003cbr\u003e Index.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402699710807,"sku":"9780471968238","price":193.46,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471968238.jpg?v=1730481275"},{"product_id":"directed-algebraic-topology-9780521760362","title":"Directed Algebraic Topology","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe first authored book to be dedicated to the new field of directed algebraic topology that arose in the 1990s, in homotopy theory and in the theory of concurrent processes. The author presents its mathematical foundations, demonstrating its relation to classical algebraic topology, and explores its varied applications.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction; Part I. First Order Directed Homotopy and Homology: 1. Directed structures and first order homotopy properties; 2. Directed homology and noncommutative geometry; 3. Modelling the fundamental category; Part II. Higher Directed Homotopy Theory: 4. Settings for higher order homotopy; 5. Categories of functors and algebras, relative settings; 6. Elements of weighted algebraic topology; Appendix A. Some points of category theory; References; Index of symbols; General index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":49402975715671,"sku":"9780521760362","price":129.0,"currency_code":"GBP","in_stock":true}]},{"product_id":"graphs-on-surfaces-dualities-polynomials-and-knots-springerbriefs-in-mathematics-9781461469704","title":"Graphs on Surfaces Dualities Polynomials and","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003e \u003ci\u003eGraphs on Surfaces: Dualities, Polynomials, and Knots\u003c\/i\u003e  also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knot theorists.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e“Here, the venerable knot-theoretic and graph-theoretic themes find a host of unifying common generalizations. Undergraduates will appreciate the patient and visual development of the foundations, particularly the dualities (paired representations of a single structure). Summing Up: Recommended. Upper-division undergraduates through researchers\/faculty.” (D. V. Feldman, Choice, Vol. 51 (7), March, 2014)\u003c\/p\u003e\u003cp\u003e“This monograph is aimed at researchers both in graph theory and in knot theory. It should be accessible to a graduate student with a grounding in both subjects. There are (colour) diagrams throughout. … The monograph gives a unified treatment of various ideas that have been studied and used previously, generalising many of them in the process.” (Jessica Banks, zbMATH, Vol. 1283, 2014)\u003c\/p\u003e\u003cp\u003e“The authors have composed a very interesting and valuable work. … For properly prepared readers … the book under review is the occasion for all sorts of fun including the inner life of ribbon groups, Tait graphs, Penrose polynomials, Tutte polynomials, and of course Jones polynomials and HOMFLY polynomials. This is fascinating mathematics, presented in a clear and accessible way.” (Michael Berg, MAA Reviews, October, 2013)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003e1. Embedded Graphs .- 2. Generalised Dualities .- 3. Twisted duality, cycle family graphs, and embedded graph equivalence .- 4. Interactions with Graph Polynomials .- 5. Applications to Knot Theory .- References .- Index . \u003c\/p\u003e","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":49408624689495,"sku":"9781461469704","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781461469704.jpg?v=1730503582"},{"product_id":"basic-algebraic-topology-9781466562431","title":"Basic Algebraic Topology","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eBuilding on rudimentary knowledge of real analysis, point-set topology, and basic algebra, \u003cstrong\u003eBasic Algebraic Topology\u003c\/strong\u003e provides plenty of material for a two-semester course in algebraic topology. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe book first introduces the necessary fundamental concepts, such as relative homotopy, fibrations and cofibrations, category theory, cell complexes, and simplicial complexes. It then focuses on the fundamental group, covering spaces and elementary aspects of homology theory. It presents the central objects of study in topology visualization: manifolds. After developing the homology theory with coefficients, homology of the products, and cohomology algebra, the book returns to the study of manifolds, discussing Poincaré duality and the De Rham theorem. A brief introduction to cohomology of sheaves and Cech cohomology follows. The core of the text covers higher homotopy groups, Hurewicz's isomorphism theorem, obstruction theory, Eilenberg-Mac Lane spaces, and Moo\u003cbr\u003e\u003cbr\u003e\u003c\/p\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e\"… a good graduate text: the book is well written and there are many well-chosen examples and a decent number of exercises. It meets its ambitious goals and should succeed in leading a lot of solid graduate students, as well as working mathematicians from other specialties seeking to learn this subject, deeper and deeper into its workings and subtleties.\"\u003cbr\u003e—Michael Berg, \u003cem\u003eMAA Reviews\u003c\/em\u003e, February 2014\u003c\/p\u003e\u003cp\u003e\"Similar to his other well-written textbook on differential topology, Professor Shastri’s book gives a detailed introduction to the vast subject of algebraic topology together with an abundance of carefully chosen exercises at the end of each chapter. The content of Professor Shastri’s book furnishes the necessary background to access many major achievements … [and] to explore current research works as well as possible applications to other branches of mathematics of modern algebraic topology.\"\u003cbr\u003e—From the Foreword by Professor Peter Wong, Bates College, Lewiston, Maine, USA\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003eIntroduction. Cell Complexes and Simplicial Complexes. Covering Spaces and Fundamental Group. Homology Groups. Topology of Manifolds. Universal Coefficient Theorem for Homology. Cohomology. Homology of Manifolds. Cohomology of Sheaves. Homotopy Theory. Homology of Fiber Spaces. Characteristic Classes. Spectral Sequences. Hints and Solutions. Bibliography. Index.\u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49408669450583,"sku":"9781466562431","price":105.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781466562431.jpg?v=1791471650"},{"product_id":"measure-and-category-9781468493412","title":"Measure and Category","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eOxtoby Bryn Mawr, April 1980 Preface to the First Edition This book has two main themes: the Baire category theorem as a method for proving existence, and the \"duality\" between measure and category.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1. Measure and Category on the Line.- Countable sets, sets of first category, nullsets, the theorems of Cantor, Baire and Borel.- 2. Liouville Numbers.- Algebraic and transcendental numbers, measure and category of the set of Liouville numbers.- 3. Lebesgue Measure in r-Space.- Definitions and principal properties, measurable sets, the Lebesgue density theorem.- 4. The Property of Baire.- Its analogy to measurability, properties of regular open sets.- 5. Non-Measurable Sets.- Vitali sets, Bernstein sets, Ulam’s theorem, inaccessible cardinals, the continuum hypothesis.- 6. The Banach-Mazur Game.- Winning strategies, category and local category, indeterminate games.- 7. Functions of First Class.- Oscillation, the limit of a sequence of continuous functions, Riemann integrability.- 8. The Theorems of Lusin and Egoroff.- Continuity of measurable functions and of functions having the property of Baire, uniform convergence on subsets.- 9. Metric and Topological Spaces.- Definitions, complete and topologically complete spaces, the Baire category theorem.- 10. Examples of Metric Spaces.- Uniform and integral metrics in the space of continuous functions, integrable functions, pseudo-metric spaces, the space of measurable sets.- 11. Nowhere Differentiable Functions.- Banach’s application of the category method.- 12. The Theorem of Alexandroff.- Remetrization of a G? subset, topologically complete subspaces.- 13. Transforming Linear Sets into Nullsets.- The space of automorphisms of an interval, effect of monotone substitution on Riemann integrability, nullsets equivalent to sets of first category.- 14. Fubini’s Theorem.- Measurability and measure of sections of plane measurable sets.- 15. The Kuratowski-Ulam Theorem.- Sections of plane sets having the property of Baire, product sets, reducibility to Fubini’s theorem by means of a product transformation.- 16. The Banach Category Theorem.- Open sets of first category or measure zero, Montgomery’s lemma, the theorems of Marczewski and Sikorski, cardinals of measure zero, decomposition into a nullset and a set of first category.- 17. The Poincaré Recurrence Theorem.- Measure and category of the set of points recurrent under a nondissipative transformation, application to dynamical systems.- 18. Transitive Transformations.- Existence of transitive automorphisms of the square, the category method.- 19. The Sierpinski-Erdös Duality Theorem.- Similarities between the classes of sets of measure zero and of first category, the principle of duality.- 20. Examples of Duality.- Properties of Lusin sets and their duals, sets almost invariant under transformations that preserve nullsets or category.- 21. The Extended Principle of Duality.- A counter example, product measures and product spaces, the zero-one law and its category analogue.- 22. Category Measure Spaces.- Spaces in which measure and category agree, topologies generated by lower densities, the Lebesgue density topology.- Supplementary Notes and Remarks.- References.- Supplementary References.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":49408677511511,"sku":"9781468493412","price":49.49,"currency_code":"GBP","in_stock":false}]},{"product_id":"elon-lima-selected-papers-9783030518172","title":"Elon Lima - Selected Papers","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis book contains all research papers published by the distinguished Brazilian mathematician Elon Lima. It includes the papers from his PhD thesis on homotopy theory, which are hard to find elsewhere. Elon Lima wrote more than 40 books in the field of topology and dynamical systems. He was a profound mathematician with a genuine vocation to teach and write mathematics.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003eComments on some mathematical contributions of Elon Lima.- The Spanier-Whitehead duality in new homotopy categories.- Stable Postnikov invariants and their duals.- Commuting vector fields on 2-manifolds.- On the local triviality of the restriction map for embeddings.- Commuting vector fields on S2.- Common singularities of commuting vector fields on 2-manifolds.- Commuting vector fields on S3.- Isometric immersions with semi-definite second quadratic forms.- Immersions of manifolds with non-negative sectional curvatures.- Orientability of smooth hypersurfaces and the Jordan-Brouwer separation theorem.- The Jordan-Brouwer separation theorem for smooth hypersurfaces. \u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e  \u003cp\u003e\u003cbr\u003e\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415622426967,"sku":"9783030518172","price":42.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030518172.jpg?v=1791480494"},{"product_id":"coherent-sheaves-superconnections-and-riemann-roch-grothendieck-9783031272332","title":"Coherent Sheaves, Superconnections, and","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck  theorem.  One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections.  Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis, by combining local index theory with the hypoelliptic Laplacian.\u003cbr\u003e\u003ci\u003eCoherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck\u003c\/i\u003e is an important contribution to both the geometric and analytic study of complex manifolds and, as such, it will be a valuable resource for many researchers in geometry, analysis, and mathematical physics. \u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction.- Bott-Chern Cohomology and Characteristic Classes.- The Derived Category ${\\mathrm{D^{b}_{\\mathrm{coh}}}}$.- Preliminaries on Linear Algebra and Differential Geometry.- The Antiholomorphic Superconnections of Block.- An Equivalence of Categories.- Antiholomorphic Superconnections and Generalized Metrics.- Generalized Metrics and Chern Character Forms.- The Case of Embeddings.- Submersions and Elliptic Superconnections.- Elliptic Superconnection Forms and Direct Images.- A Proof of Theorem 10-1 when $\\overline{\\partial}^{X}\\partial^{X}\\omega^{X}=0$..- The Hypoelliptic Superconnections.- The Hypoelliptic Superconnection Forms.-  The Hypoelliptic Superconnection Forms when $\\overline{\\partial}^{X}\\partial^{X}\\omega^{X}=0$.-  Exotic Superconnections and Riemann-Roch-Grothendieck.- Subject Index.- Index of Notation.- Bibliography.","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":49415703494999,"sku":"9783031272332","price":98.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031272332.jpg?v=1730527847"},{"product_id":"collected-papers-gesammelte-abhandlungen-9783642383687","title":"Collected Papers - Gesammelte Abhandlungen","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eFrom the preface: \"Hopf algebras, Hopf fibration of spheres, Hopf-Rinow complete Riemannian manifolds, Hopf theorem on the ends of groups - can one imagine modern mathematics without all this? Many other concepts and methods, fundamental in various mathematical disciplines, also go back directly or indirectly to the work of Heinz Hopf: homological algebra, singularities of vector fields and characteristic classes, group-like spaces, global differential geometry, and the whole algebraisation of topology with its influence on group theory, analysis and algebraic geometry. It is astonishing to realize that this oeuvre of a whole scientific life consists of only about 70 writings. Astonishing also the transparent and clear style, the concreteness of the problems, and how abstract and far-reaching the methods Hopf invented.\"\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e \u003c\/p\u003e \u003cp\u003eHeinz Hopf (1894-1981) is rightly considered to be one of the outstanding and most influential mathematicians of the XXth century. He was a pioneer in algebraic topology as well as in differential geometry. He is widely known as having studied the ‘Hopf fibration’. The very general abstract notion of Hopf algebra was introduced as tracing in Hopf’s works; he may be considered to have been a forerunner of the creation of homological algebra. He found a noncontractible map of the 3-sphere into the 2-sphere; that result was an essential step towards the concept of ‘Hopf invariant’ and the popularization of the homotopy group notion due to Hurewicz. \u003c\/p\u003e \u003cp\u003eHeinz Hopf was born in Wroclaw (Breslau), in the then German part of Poland. He studied in his home town, in Heidelberg and in Berlin, visited Göttingen, Princeton University, and finally settled at ETH in Zürich, where he became Weyl’s successor.\u003c\/p\u003e \u003cp\u003eThe Heinz Hopf Selecta published in 1964 contained an important – although far from being complete – part of Hopf’s mathematical production. So this volume presenting Hopf’s collected works is welcome. As one may expect, the organisational achievement by Beno Eckmann, Hopf’s student and friend, is high class. Two important articles are translated from German into English.\u003c\/p\u003e \u003cp\u003eThis book of over 1200 pages featuring 71 items constitutes an essential reference for the development of mathematics during the XXth century.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eJean-Paul Pier (Zbl. MATH 980, 01027)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eTable of Contents.- List of Publications of Heinz Hopf.- Editor's Preface.- Papers of Heinz Hopf.- Heinz Hopf Selecta.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":49420036702551,"sku":"9783642383687","price":52.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783642383687.jpg?v=1730540557"},{"product_id":"basic-algebraic-topology-and-its-applications-9788132238553","title":"Basic Algebraic Topology and its Applications","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike.\u003cbr\u003eFocusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003e“Adhikari’s work is an excellent resource for any individual seeking to learn more about algebraic topology. By no means will this text feel like an introduction to algebraic topology, but it does offer much for both beginners and experts. … the text will be a valuable reference on the bookshelf of any reader with an interest in algebraic topology. Summing Up: Recommended. Upper-division undergraduates and above; researchers and faculty.” (A. Misseldine, Choice, Vol. 54 (9), May, 2017)\u003c\/p\u003e\u003cp\u003e“I am pretty enthusiastic about this book. … it shows very good taste on the author’s part as far as what he’s chosen to do and how he’s chosen to do it. … Wow! What a nice book. I’m glad I have a copy.” (Michael Berg, MAA Reviews, maa.org, February, 2017)\u003c\/p\u003e“This is a comprehensive textbook on algebraic topology. … accessible to students of all levels of mathematics, so suitable for anyone wanting and needing to learn about algebraic topology. It can also offer a valuable resource for advanced students with a specialized knowledge in other areas who want to pursue their interest in this area. … further readings are provided at the end of each of them, which also enables students to study the subject discussed therein in more depth.” (Haruo Minami, zbMATH 1354.55001, 2017)\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003ePrerequisite Concepts and Notations.- Basic Homotopy.- The Fundamental Groups.-Covering Spaces.- Fibre Bundles, Vector Bundles and K-theory.- Geometry of Simplicial Complexes and Fundamental Groups.- Higher Homotopy Groups.- Products in Higher Homotopy Groups.- CW-complexes and Homotopy.- Eilenberg-MacLane Spaces.- Homology and Cohomology Theories.- Eilenberg-Steenrod Axioms for Homology and Cohomology Theories.- Consequences of the Eilenberg-Steenrod Axioms.- Some Applications of Homology Theory.- Spectral Homology and Cohomology Theories.- Obstruction Theory.- More Relations Between Homotopy and Homology Groups.- A Brief Historical Note.\u003c\/p\u003e","brand":"Springer, India, Private Ltd","offers":[{"title":"Default Title","offer_id":49427249365335,"sku":"9788132238553","price":62.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9788132238553.jpg?v=1791482658"},{"product_id":"rigid-germs-the-valuative-tree-and-applications-to-kato-varieties-9788876425585","title":"Rigid Germs, the Valuative Tree, and Applications","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis thesis deals with specific features of the theory of holomorphic dynamics in dimension 2 and then sets out to study analogous questions in higher dimensions, e.g. dealing with normal forms for rigid germs, and examples of Kato 3-folds.\u003c\/p\u003e\u003cp\u003eThe local dynamics of holomorphic maps around critical points is still not completely understood, in dimension 2 or higher, due to the richness of the geometry of the critical set for all iterates.\u003c\/p\u003e\u003cp\u003eIn dimension 2, the study of the dynamics induced on a suitable functional space (the valuative tree) allows a classification of such maps up to birational conjugacy, reducing the problem to the special class of rigid germs, where the geometry of the critical set is simple.\u003c\/p\u003e\u003cp\u003e      \u003c\/p\u003e\u003cp\u003eIn some cases, from such dynamical data one can construct special compact complex surfaces, called Kato surfaces, related to some conjectures in complex geometry.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003eIntroduction.-1.Background.- 2.Dynamics in 2D.- 3.Rigid germs in higher dimension.- 4 Construction of non-Kahler 3-folds.- References.- Index.\u003c\/p\u003e","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":49427425755479,"sku":"9788876425585","price":13.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9788876425585.jpg?v=1730564501"},{"product_id":"algebra-3-homological-algebra-and-its-applications-9789813363250","title":"Algebra 3: Homological Algebra and Its","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis book, the third book in the four-volume series in algebra, deals with important topics in homological algebra, including abstract theory of derived functors, sheaf co-homology, and an introduction to etale and l-adic co-homology. It contains four chapters which discuss homology theory in an abelian category together with some important and fundamental applications in geometry, topology, algebraic geometry (including basics in abstract algebraic geometry), and group theory. The book will be of value to graduate and higher undergraduate students specializing in any branch of mathematics. The author has tried to make the book self-contained by introducing relevant concepts and results required. Prerequisite knowledge of the basics of algebra, linear algebra, topology, and calculus of several variables will be useful.\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e“This is an excellent book on Homological Algebra. All topics dealt here are presented in a very\u003cbr\u003e systematic way. It is an ideal handbook for any person desirous of pursuing research in Homological Algebra. … At the end of each section of each chapter an exhaustive list of exercises is given.” (Veereshwar A. Hiremath, zbMATH 1474.01001, 2021)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eChapter 1. Homological Algebra 1.- Chapter 2. Homological Algebra 2, Derived Functions.- Chapter 3. Homological Algebra 3, Examples and Applications.- Chapter 4. Sheaf Co-homology and Applications.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":49427857244503,"sku":"9789813363250","price":35.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789813363250.jpg?v=1791484182"},{"product_id":"lefschetz-properties-9789819738854","title":"Lefschetz Properties","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eSurvey articles about specific topics.- Jordan types and relation with WLP\/SLP.- Unexpected objects, connections with Lefschetz properties and special sets of points.- Combinatorial aspects.- Working group on Perazzo hypersurfaces Hilbert functions, WLP, Jordan types.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":49427873628503,"sku":"9789819738854","price":134.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789819738854.jpg?v=1730565971"},{"product_id":"algebraic-topology-9780521795401","title":"Algebraic Topology","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eIn most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.  The four main chapters present the basic material of the subject: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature of the book is the inclusion of many optional topics which are not usually part of a first course due to time constraints, and for which elementary expositions are sometimes hard to find. Among these are: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James r\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'… this is a marvellous tome, which is indeed a delight to read. This book is destined to become very popular amongst students and teachers alike.' Bulletin of the Belgian Mathematical Society\u003cbr\u003e'… clear and concise … makes the book useful both as a basis for courses and as a reference work.' Monatshefte für Mathematik\u003cbr\u003e'… the truly unusual abundance of instructive examples and complementing exercises is absolutely unique of such a kind … the distinctly circumspect, methodologically inductive, intuitive, descriptively elucidating and very detailed style of writing give evidence to the fact that the author's first priorities are exactly what students need when working with such a textbook, namely clarity, readability, steady motivation, guided inspiration, increasing demand, and as much self-containedness of the exposition as possible. No doubt, a very devoted and experienced teacher has been at work here, very much so to the benefit of beginners in the field of algebraic topology, instructors, and interested readers in general.' Zentralblatt MATH\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePart I. Some Underlying Geometric Notions: 1. Homotopy and homotopy type; 2. Deformation retractions; 3. Homotopy of maps; 4. Homotopy equivalent spaces; 5. Contractible spaces; 6. Cell complexes definitions and examples; 7. Subcomplexes; 8. Some basic constructions; 9. Two criteria for homotopy equivalence; 10. The homotopy extension property; Part II. Fundamental Group and Covering Spaces: 11. The fundamental group, paths and homotopy; 12. The fundamental group of the circle; 13. Induced homomorphisms; 14. Van Kampen's theorem of free products of groups; 15. The van Kampen theorem; 16. Applications to cell complexes; 17. Covering spaces lifting properties; 18. The classification of covering spaces; 19. Deck transformations and group actions; 20. Additional topics: graphs and free groups; 21. K(G,1) spaces; 22. Graphs of groups; Part III. Homology: 23. Simplicial and singular homology delta-complexes; 24. Simplicial homology; 25. Singular homology; 26. Homotopy invariance; 27. Exact sequences and excision; 28. The equivalence of simplicial and singular homology; 29. Computations and applications degree; 30. Cellular homology; 31. Euler characteristic; 32. Split exact sequences; 33. Mayer–Vietoris sequences; 34. Homology with coefficients; 35. The formal viewpoint axioms for homology; 36. Categories and functors; 37. Additional topics homology and fundamental group; 38. Classical applications; 39. Simplicial approximation and the Lefschetz fixed point theorem; Part IV. Cohomology: 40. Cohomology groups: the universal coefficient theorem; 41. Cohomology of spaces; 42. Cup product the cohomology ring; 43. External cup product; 44. Poincaré duality orientations; 45. Cup product; 46. Cup product and duality; 47. Other forms of duality; 48. Additional topics the universal coefficient theorem for homology; 49. The Kunneth formula; 50. H-spaces and Hopf algebras; 51. The cohomology of SO(n); 52. Bockstein homomorphisms; 53. Limits; 54. More about ext; 55. Transfer homomorphisms; 56. Local coefficients; Part V. Homotopy Theory: 57. Homotopy groups; 58. The long exact sequence; 59. Whitehead's theorem; 60. The Hurewicz theorem; 61. Eilenberg–MacLane spaces; 62. Homotopy properties of CW complexes cellular approximation; 63. Cellular models; 64. Excision for homotopy groups; 65. Stable homotopy groups; 66. Fibrations the homotopy lifting property; 67. Fiber bundles; 68. Path fibrations and loopspaces; 69. Postnikov towers; 70. Obstruction theory; 71. Additional topics: basepoints and homotopy; 72. The Hopf invariant; 73. Minimal cell structures; 74. Cohomology of fiber bundles; 75. Cohomology theories and omega-spectra; 76. Spectra and homology theories; 77. Eckmann-Hilton duality; 78. Stable splittings of spaces; 79. The loopspace of a suspension; 80. Symmetric products and the Dold–Thom theorem; 81. Steenrod squares and powers; Appendix: topology of cell complexes; The compact-open topology.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":49525470069079,"sku":"9780521795401","price":36.09,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780521795401.jpg?v=1731860627"},{"product_id":"algebra-in-the-stone-cech-compactification-theory-and-applications-9783110256239","title":"Algebra in the Stone-Cech Compactification:","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis is the second revised and extendededition of the successful book on the algebraic structure of the Stone-Čech compactification of a discrete semigroup and its combinatorial applications, primarily in the field known as Ramsey Theory. There has been very active research in the subject dealt with by the book in the 12 years which is now included in this edition.    This book is a self-contained exposition of the theory of compact right semigroupsfor discrete semigroups and the algebraic properties of these objects. The methods applied in the book constitute a mosaic of infinite combinatorics, algebra, and topology. The reader will find numerous combinatorial applications of the theory, including the central sets theorem, partition regularity of matrices, multidimensional Ramsey theory, and many more.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eThe present book is the first devoted to an extensive study of the algebraic structure of sS and the many applications thereof; it is an exciting book, written - and very well written - by two mathematicians who are eminently qualified two write it, and it is essentially self-contained, requiring only that the reader come to it with the basic concepts of first graduate courses in algebra, analysis and topology. I recommend this book highly; it will be very useful, both to researchers and to students. Its index, list of symbols and up-to-date bibliography are very helpful. Paul Milnes, Zentralblatt MATH \/ 1998  The authors present a self-contained exposition. The book under review is written by two mathematicians who have contributed in a decisive way to this rapidly expanding area and provides a unique opportunity to obtain a 'colorful' panoramic view of the subject. Michael Tkacenko, MathSciNet \/ 1999","brand":"De Gruyter","offers":[{"title":"Default Title","offer_id":49537152581975,"sku":"9783110256239","price":64.6,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783110256239.jpg?v=1731905466"},{"product_id":"functions-of-several-complex-variables-and-their-singularities-9780821833193","title":"Functions of Several Complex Variables and Their","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003ePresents an introduction to the theory of functions of several complex variables and their singularities, with special emphasis on topological aspects. This book includes such topics as Riemann surfaces, holomorphic functions of several variables, classification and deformation of singularities, and fundamentals of differential topology.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eRiemann surfaces Holomorphic functions of several variables Isolated singularities of holomorphic functions Fundamentals of differential topology Topology of singularities Bibliography Index.","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":49963655659863,"sku":"9780821833193","price":78.3,"currency_code":"GBP","in_stock":true}]},{"product_id":"knots-and-surfaces-9780821804513","title":"Knots and Surfaces","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eLeads readers to discover some real mathematics. This book is suitable for a one-semester course at the beginning undergraduate level.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eNetworks (Chapter 1) Surfaces (Chapter 2) Knots (Chapter 3) Projects (Chapter 4) Bibliography Index.","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":49963662410071,"sku":"9780821804513","price":36.05,"currency_code":"GBP","in_stock":true}]},{"product_id":"introduction-to-topological-manifolds-9781441979391","title":"Introduction to Topological Manifolds","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological                            ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields.\u003c\/p\u003e\u003cp\u003eAlthough this second edition has the same basic                            structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on                            simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003eFrom the reviews of the second edition:\u003c\/p\u003e\u003cp\u003e“An excellent introduction to both point-set and algebraic topology at the early-graduate level, using manifolds as a primary source of examples and motivation. … The author has … fulfilled his objective of integrating a study of manifolds into an introductory course in general and algebraic topology. This text is well-organized and clearly written, with a good blend of motivational discussion and mathematical rigor. … Any student who has gone through this book should be well-prepared to pursue the study of differential geometry … .” (Mark Hunacek, The Mathematical Association of America, March, 2011)\u003c\/p\u003e\u003cp\u003e“This book is designed for first year graduate students as an introduction to the topology of manifolds. … The book can be read with advantage by any graduate student with a good undergraduate background, and indeed by many upper class undergraduates. It can be used for self study or as a text book for a fine geometrically flavored introduction to manifolds. One which provides excellent motivation for studying the machinery needed for more advanced work.” (Jonathan Hodgson, Zentralblatt MATH, Vol. 1209, 2011)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003ePreface.- 1 Introduction.- 2 Topological Spaces.- 3 New Spaces from Old.- 4 Connectedness and Compactness.- 5 Cell Complexes.- 6 Compact Surfaces.- 7 Homotopy and the Fundamental Group.- 8 The Circle.- 9 Some Group Theory.- 10 The Seifert-Van Kampen Theorem.- 11 Covering Maps.- 12 Group Actions and Covering Maps.- 13 Homology.- Appendix A: Review of Set Theory.- Appendix B: Review of Metric Spaces.- Appendix C: Review of Group Theory.- References.- Notation Index.- Subject Index.\u003c\/p\u003e","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":50029425459543,"sku":"9781441979391","price":48.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781441979391.jpg?v=1740090024"},{"product_id":"homotopy-of-operads-and-grothendieckteichmuller-groups-9781470434816","title":"Homotopy of Operads and GrothendieckTeichmuller","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eFrom operads to Grothendieck-Teichmuller groups. The general theory of operads: The basic concepts of the theory of operads\u003c\/li\u003e\n\u003cli\u003eThe definition of operadic composition structures revisited\u003c\/li\u003e\n\u003cli\u003eSymmetric monoidal categories and operads\u003c\/li\u003e\n\u003cli\u003eBraids and $E_n$-operads: The little discs model of $E_n$-operads\u003c\/li\u003e\n\u003cli\u003eBraids and the recognition of $E_2$-operads\u003c\/li\u003e\n\u003cli\u003eThe magma and parenthesized braid operators\u003c\/li\u003e\n\u003cli\u003eHopf algebras and the Malcev completion: Hopf algebras\u003c\/li\u003e\n\u003cli\u003eThe Malcev completion for groups\u003c\/li\u003e\n\u003cli\u003eThe Malcev completion for groupoids and operads\u003c\/li\u003e\n\u003cli\u003eThe operadic definition of the Grothendieck-Teichmuller group: The Malcev completion of the braid operads and Drinfeld's associators\u003c\/li\u003e\n\u003cli\u003eThe Grothendieck-Teichmuller group\u003c\/li\u003e\n\u003cli\u003eA glimpse at the Grothendieck program\u003c\/li\u003e\n\u003cli\u003eAppendices: Trees and the construction of free operads\u003c\/li\u003e\n\u003cli\u003eThe cotriple resolution of operads\u003c\/li\u003e\n\u003cli\u003eGlossary of notation\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50041317720407,"sku":"9781470434816","price":103.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470434816.jpg?v=1740182212"},{"product_id":"computational-aspects-of-discrete-subgroups-of-lie-groups-9781470468040","title":"Computational Aspects of Discrete Subgroups of","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003ePresents the proceedings of the virtual workshop on Computational Aspects of Discrete Subgroups of Lie Groups, held in June 2021. The major theme deals with a novel domain of computational algebra: the design, implementation, and application of algorithms based on matrix representation of groups and their geometric properties.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cul\u003e\n\u003cli\u003eD. Gabai, R. Meyerhoff, N. Thurston, and A. Yarmola, Enumerating Kleinian groups\u003c\/li\u003e\n\u003cli\u003eW. A. de Graaf, Exploring Lie theory with GAP\u003c\/li\u003e\n\u003cli\u003eA. S. Detinko, D. L. Flannery, and A. Hulpke, Freeness and $S$-arithmeticity of rational Mobius groups\u003c\/li\u003e\n\u003cli\u003eJ. Gilman, Computability models: Algebraic, topological and geometric algorithms\u003c\/li\u003e\n\u003cli\u003eW. M. Goldman, Compact components of planar surface group representations\u003c\/li\u003e\n\u003cli\u003eA. Hulpke, Proving infinite index for a subgroup of matrices\u003c\/li\u003e\n\u003cli\u003eM. Kapovich, Geometric algorithms for discreteness and faithfulness\u003c\/li\u003e\n\u003cli\u003eM. Kapovich, A. Detinko, and A. Kontorovich, List of problems on discrete subgroups of Lie groups and their computational aspects\u003c\/li\u003e\n\u003cli\u003eA. Mark, J. Paupert, and D. Polletta, Picard modular groups generated by complex reflections\u003c\/li\u003e\n\u003cli\u003eJ. M. Riestenberg, Verifying the straight-and-spaced condition\u003c\/li\u003e\n\u003cli\u003eT. N. Venkataramana, Unipotent generators for arithmetic groups\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50046683971927,"sku":"9781470468040","price":97.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470468040.jpg?v=1740272105"},{"product_id":"integer-and-polynomial-algebra-9781470473327","title":"Integer and Polynomial Algebra","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eOffers a concrete introduction to abstract algebra and number theory. Starting from the basics, it develops the rich parallels between the integers and polynomials, covering topics such as Unique Factorization, arithmetic over quadratic number fields, the RSA encryption scheme, and finite fields.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cul\u003e\n\u003cli\u003eThe integers\u003c\/li\u003e\n\u003cli\u003eModular arithmetic\u003c\/li\u003e\n\u003cli\u003eDiophantine equations and quadratic number domains\u003c\/li\u003e\n\u003cli\u003eCodes and factoring\u003c\/li\u003e\n\u003cli\u003eReal and complex numbers\u003c\/li\u003e\n\u003cli\u003eThe ring of polynomials\u003c\/li\u003e\n\u003cli\u003eFinite fields\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50046691475799,"sku":"9781470473327","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470473327.jpg?v=1740272339"},{"product_id":"algebraic-topology-9783111517360","title":"Algebraic Topology","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"De Gruyter","offers":[{"title":"Default Title","offer_id":50470557221207,"sku":"9783111517360","price":104.02,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783111517360.jpg?v=1782125549"},{"product_id":"algebraic-topology-a-primer-9789386279675","title":"Algebraic Topology: A Primer","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis is the second (revised and enlarged) edition of the book originally published in 2003. It introduces the first concepts of Algebraic Topology like general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in detail. The text has been designed for undergraduate and beginning graduate students of Mathematics. It assumes a minimal background of linear algebra, group theory and topological spaces.  The author has dealt with the basic concepts and ideas in a very lucid manner giving suitable motivations and illustrations. As an application of the tools developed in this book, some classical theorems like Brouwer’s fixed point theorem, the Lefschetz fixed point theorem, the Borsuk-Ulam theorem, Brouwer’s separation theorem and the theorem on invariance of domain have been proved and illustrated. Most of the exercises are elementary but some are more challenging and will help the readers in their understanding of the subject.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cul\u003e\n\u003cli\u003e1 Basic Topology: A review \u003c\/li\u003e\n\u003cli\u003e2 The Fundamental Group\u003c\/li\u003e\n\u003cli\u003e3 Simplicial Complexes\u003c\/li\u003e\n\u003cli\u003e4 Simplicial Homology \u003c\/li\u003e\n\u003cli\u003e5 Covering Projections \u003c\/li\u003e\n\u003cli\u003e6 Singular Homology\u003c\/li\u003e\n\u003cli\u003e7 Appendix\u003c\/li\u003e\n\u003cli\u003eReferences\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Jainendra K Jain","offers":[{"title":"Default Title","offer_id":50473222799703,"sku":"9789386279675","price":44.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789386279675.jpg?v=1744905768"},{"product_id":"nonlinear-dynamics-and-time-series-building-a-bridge-between-the-natural-and-statistical-sciences-9780821841853","title":"Nonlinear Dynamics and Time Series  Building a","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eA collection of research and expository papers reflecting the interfacing of two fields: nonlinear dynamics and statistics. It presents the proceedings of a workshop entitled 'Nonlinear Dynamics and Time Series: Building a Bridge Between the Natural and Statistical Sciences' held at the Centre de Recherches Mathematiques in Montreal in July 1995.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eOpening lectures: Tools for the analysis of chaotic data by H. I. Abarbanel Some comments on nonlinear time series analysis by H. Tong Embeddings, dimension, and system reconstruction: A general approach to predictive and fractal scaling dimensions in discrete-index time series by C. D. Cutler Statistics for continuity and differentiability: An application to attractor reconstruction from time series by L. M. Pecora, T. L. Carroll, and J. F. Heagy Reconstruction of integrate-and-fire dynamics by T. Sauer Surrogate data methodology: On the validity of the method of surrogate data by K.-S. Chan Using \"surrogate surrogate data\" to calibrate the actual rate of false positives in tests for nonlinearity in time series by J. Theiler and D. Prichard Local Lyapunov exponents: Chaos with confidence: Asymptotics and applications of local Lyapunov exponents by B. A. Bailey, S. Ellner, and D. W. Nychka Estimating local Lyapunov exponents by Z.-Q. Lu and R. L. Smith Long-range dependence: Defining and measuring long-range dependence by P. Hall Modelling nonlinearity and long memory in time series by P. M. Robinson and P. Zaffaroni Data analysis and applications: Ergodic distributions of random dynamical systems by L. M. Berliner, S. N. MacEachern, and C. S. Forbes Detecting structure in noise by L. Borland Characterizing nonlinearity in weather and epilepsy data: A personal view by M. C. Casdagli Assessment of linear and nonlinear correlations between neural firing events by A. Longtin and D. M. Racicot Markov chain methods in the analysis of heart rate variability by S. J. Merrill and J. R. Cochran.","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50577673683287,"sku":"9780821841853","price":81.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780821841853.jpg?v=1746096121"},{"product_id":"homotopy-theory-and-arithmetic-geometry-motivic-and-diophantine-aspects-lms-cmi-research-school-london-july-2018-9783030789763","title":"Homotopy Theory and Arithmetic Geometry – Motivic","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry.   \u003cp\u003eThe contributions to this volume are based on original lectures by leading researchers at the LMS-CMI Research School on ‘Homotopy Theory and Arithmetic Geometry - Motivic and Diophantine Aspects’ and the Nelder Fellow Lecturer Series, which both took place at Imperial College London in the summer of 2018. The contribution by Brazelton, based on the lectures by Wickelgren, provides an introduction to arithmetic enumerative geometry, the notes of Cisinski present motivic sheaves and new cohomological methods for intersection theory, and Schlank’s contribution gives an overview of the use of étale homotopy theory for obstructions to the existence of rational points on algebraic varieties. Finally, the article by Asok and Østvær, based in part on the Nelder Fellow lecture series by Østvær, gives a survey of the interplay between motivic homotopy theory and affine algebraic geometry, with a focus on contractible algebraic varieties.\u003c\/p\u003e \u003cp\u003eNow a major trend in arithmetic geometry, this volume offers a detailed guide to the fascinating circle of recent applications of homotopy theory to number theory. It will be invaluable to research students entering the field, as well as postdoctoral and more established researchers.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e- 1. Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects: an Introduction.- 2. An Introduction to \u003cb\u003eA\u003c\/b\u003e\u003csup\u003e1\u003c\/sup\u003e-Enumerative Geometry.- 3. Cohomological Methods in Intersection Theory.- 4. Étale Homotopy and Obstructions to Rational Points.- 5. \u003cb\u003eA\u003c\/b\u003e\u003csup\u003e1\u003c\/sup\u003e-Homotopy Theory and Contractible Varieties: a Survey.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":50578714788183,"sku":"9783030789763","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030789763.jpg?v=1791480535"},{"product_id":"algebraic-topology-homotopy-and-homology-9783540427506","title":"Algebraic Topology - Homotopy and Homology","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eFrom the reviews: \"The author has attempted an ambitious and most commendable project. […] The book contains much material that has not previously appeared in this format. The writing is clean and clear and the exposition is well motivated. [...] This book is, all in all, a very admirable work and a valuable addition to the literature.\" Mathematical Reviews \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003e\"This book contains much impressive mathematics, namely the achievements by algebraic topologists in obtaining extensive information on the stable homotopy groups of spheres, and the computation of various cobordism groups. It is a long book, and for the major part a very advanced book. ... (It is) suitable for specialists, or for those who already know what algebraic topology is for, and want a guide to the principal methods of stable homotopy theory.\"\u003cbr\u003eR. Brown in Bulletin of the London Mathematical Society, 1980\u003c\/p\u003e \u003cp\u003e\"In the more than twenty five years since its first appearance, the book has met with favorable response, both in its use as a text and as reference. It is a good course which leads the reader systematically to the point at which he can begin to tackle problems in algebraic topology. … This book remains one of the best sources for the material which every young algebraic topologist should know.\" (Corina Mohorianu, Zentralblatt MATH, Vol. 1003 (3), 2003)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eo. Some Facts from General Topology 1. Categories, Functors and Natural Transformations 2. Homotopy Sets and Groups 3. Properties of the Homotopy Groups 4. Fibrations 5. CW-Complexes 6. Homotopy Properties of CW-Complexes  7. Homology and Cohomology Theories  8. Spectra 9. Representation Theorems  10. Ordinary Homology Theory 11. Vector Bundles and K-Theory  12. Manifolds and Bordism  13. Products  14. Orientation and Duality  15. Spectral Swquences  16. Characteristic Classes  17. Cohomology Operations and Homology Cooperations  18. The Steenrod Algebra and its Dual  19. The Adams Spectral Sequence and the e-Invariant  20. Calculation of the Corbordism Groups Bibliography  Subject Index","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":50579139428695,"sku":"9783540427506","price":999.99,"currency_code":"GBP","in_stock":false}]}],"url":"https:\/\/bookcurl.com\/collections\/algebraic-topology.oembed?page=4","provider":"Book Curl","version":"1.0","type":"link"}