Algebraic topology Books
Springer Nature Switzerland AG Holomorphic Foliations with Singularities: Key
Book SynopsisThis 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.The 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.Graduate 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.Table of ContentsPreface.- 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.
£53.99
Springer Nature Switzerland AG Equivariant Cohomology of Configuration Spaces
Book SynopsisThis book gives a brief treatment of the equivariant cohomology of the classical configuration space F(ℝ^d,n) from its beginnings to recent developments. This subject has been studied intensively, starting with the classical papers of Artin (1925/1947) on the theory of braids, and progressing through the work of Fox and Neuwirth (1962), Fadell and Neuwirth (1962), and Arnol'd (1969). The focus of this book is on the mod 2 equivariant cohomology algebras of F(ℝ^d,n), whose additive structure was described by Cohen (1976) and whose algebra structure was studied in an influential paper by Hung (1990). A detailed new proof of Hung's main theorem is given, however it is shown that some of the arguments given by him on the way to his result are incorrect, as are some of the intermediate results in his paper.This invalidates a paper by three of the authors, Blagojević, Lück and Ziegler (2016), who used a claimed intermediate result in order to derive lower bounds for the existence of k-regular and ℓ-skew embeddings. Using the new proof of Hung's main theorem, new lower bounds for the existence of highly regular embeddings are obtained: Some of them agree with the previously claimed bounds, some are weaker.Assuming only a standard graduate background in algebraic topology, this book carefully guides the reader on the way into the subject. It is aimed at graduate students and researchers interested in the development of algebraic topology in its applications in geometry.Trade Review“The book is well written. … The book will be important for those who study the cohomology rings of configuration spaces.” (Shintarô Kuroki, Mathematical Reviews, November, 2022)Table of Contents- 1. Snapshots from the History. - Part I Mod 2 Cohomology of Configuration Spaces. - 2. The Ptolemaic Epicycles Embedding. - 3. The Equivariant Cohomology of Pe(Rd, 2m). - 4. Hu’ng’s Injectivity Theorem. - Part II Applications to the (Non-)Existence of Regular and SkewEmbeddings. - 5. On Highly Regular Embeddings: Revised. - 6. More Bounds for Highly Regular Embeddings. - Part III Technical Tools. - 7. Operads. - 8. The Dickson Algebra. - 9. The Stiefel–Whitney Classes of the Wreath Square of a Vector Bundle. - 10. Miscellaneous Calculations.
£42.74
Springer International Publishing AG Simplicial and Dendroidal Homotopy Theory
Book SynopsisThis open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory combines the combinatorics of trees with the theory of Quillen model categories. Dendroidal sets are a natural generalization of simplicial sets from the point of view of operads. In this book, the simplicial approach to higher category theory is generalized to a dendroidal approach to higher operad theory. This dendroidal theory of higher operads is carefully developed in this book. The book also provides an original account of the more established simplicial approach to infinity-categories, which is developed in parallel to the dendroidal theory to emphasize the similarities and differences. Simplicial and Dendroidal Homotopy Theory is a complete introduction, carefully written with the beginning researcher in mind and ideally suited for seminars and courses. It can also be used as a standalone introduction to simplicial homotopy theory and to the theory of infinity-categories, or a standalone introduction to the theory of Quillen model categories and Bousfield localization.Trade Review“This book is a readable and carefully organized account of dendroidal sets by two of the main figures in the field. It gives a self-contained, detailed description of dendroidal sets and spaces … . Each chapter is also accompanied by a short section of historical notes giving background, references, and historical perspectives on the ideas presented.” (Ben C Walter, Mathematical Reviews, December, 2023)Table of ContentsPart I The Elementary Theory of Simplicial and Dendroidal Sets.- 1 Operads.- 2 Simplicial Sets.- 3 Dendroidal Sets.- 4 Tensor Products of Dendroidal Sets.- 5 Kan Conditions for Simplicial Sets.- 6 Kan Conditions for Dendroidal Sets.- Part II The Homotopy Theory of Simplicial and Dendroidal Sets.- 7 Model Categories.- 8 Model Structures on the Category of Simplicial Sets.- 9 Three Model Structures on the Category of Dendroidal Sets.- Part III The Homotopy Theory of Simplicial and Dendroidal Spaces.- 10 Reedy Categories and Diagrams of Spaces.- 11 Mapping Spaces and Bousfield Localizations.- 12 Dendroidal Spaces and ∞-Operads.- 13 Left Fibrations and the Covariant Model Structure.- 14 Simplicial Operads and ∞-Operads.- Epilogue.- References.- Index.
£42.74
Birkhauser Verlag AG Coherent Sheaves, Superconnections, and
Book SynopsisThis 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.Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck 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. Table of ContentsIntroduction.- 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.
£98.99
Springer Toric Topology and Polyhedral Products
Book SynopsisPreface.- Connected sums of sphere products and minimally non-Golod complexes.- Toric manifolds over 3-polytopes.- Symmetric products and a Cartan-type formula for polyhedral products.- Multiparameter persistent homology via generalized Morse theory.- Compact torus action on the complex Grassmann manifolds.- On the enumeration of Fano Bott manifolds.- Dga models for moment-angle complexes.- Duality in toric topology.- Bundles over connected sums.- The SO(4) Verlinde formula using real polarizations.- GKM graph locally modelled by TnxS1-action on T*Cn and its graph equivariant cohomology.- On the genera of moment-angle manifolds associated to dual-neighborly polytopes: combinatorial formulas and sequences.- Homeomorphic model for the polyhedral smash product of disks and spheres.- Invariance of polarization induced by symplectomorphisms.- Polyhedral products for wheel graphs and their generalizations.- On the cohomology ring of real moment-angle complexes.
£107.99
Birkhäuser An Introduction to CAlgebras and Noncommutative
Book Synopsis
£43.33
De Gruyter Algebra in the Stone-Cech Compactification:
Book SynopsisThis 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.Trade ReviewThe 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
£64.60
De Gruyter Knots
Book SynopsisThis 3. edition is an introduction to classical knot theory. It contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory. Most of the topics considered in the book are developed in detail; only the main properties of fundamental groups and some basic results of combinatorial group theory are assumed to be known.
£123.98
De Gruyter Algebraic Topology
Book Synopsis
£87.60
Springer International Publishing AG A Cp-Theory Problem Book: Compactness in Function
Book SynopsisThis third volume in Vladimir Tkachuk's series on Cp-theory problems applies all modern methods of Cp-theory to study compactness-like properties in function spaces and introduces the reader to the theory of compact spaces widely used in Functional Analysis. The text is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research covering a wide variety of topics in Cp-theory and general topology at the professional level. The first volume, Topological and Function Spaces © 2011, provided an introduction from scratch to Cp-theory and general topology, preparing the reader for a professional understanding of Cp-theory in the last section of its main text. The second volume, Special Features of Function Spaces © 2014, continued from the first, giving reasonably complete coverage of Cp-theory, systematically introducing each of the major topics and providing 500 carefully selected problems and exercises with complete solutions. This third volume is self-contained and works in tandem with the other two, containing five hundred carefully selected problems and solutions. It can also be considered as an introduction to advanced set theory and descriptive set theory, presenting diverse topics of the theory of function spaces with the topology of point wise convergence, or Cp-theory which exists at the intersection of topological algebra, functional analysis and general topology.Trade Review“This volume … is a very useful book for all researchers working in Cp-theory (also in general topology) and its relationships with other mathematical disciplines, especially with functional analysis. The problems in chapter 4 can attract young mathematicians to work in this field and to solve some of quite difficult problems.” (Ljubiša D. Kočinac, zbMATH, Vol. 1325.54001, 2016)From the Reviews of Topological and Function Spaces: “…It is designed to bring a dedicated reader from the basic topological principles to the frontiers of modern research. Any reasonable course in calculus covers everything needed to understand this book. This volume can also be used as a reference for mathematicians working in or outside the field of topology (functional analysis) wanting to use results or methods of Cp-theory...On the whole, the book provides a useful addition to the literature on Cp-theory, especially at the instructional level." (Mathematical Reviews)Table of ContentsPreface.- Contents.- Detailed summary of exercise sections.- Introduction.- 1. Behavior of Compactness in Function Spaces.- 2. Solutions of Problems 001-0500.- 3. Bonus Results: Some Hidden Statements.- 4. Open Problems.- Bibliography.- List of Special Symbols.- Index.
£40.49
Springer International Publishing AG Homotopical Topology
Book SynopsisThis 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).Trade Review“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)“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)Table of ContentsIntroduction.- Homotopy.- Homology.- Spectral Sequences of Fibrations.- Cohomology Operations.- The Adams Spectral Sequence.- K-Theory and Other Extraordinary Cohomology Theories.
£47.69
Springer Fachmedien Wiesbaden Algebraische Topologie: Eine Einführung
Book SynopsisI Geometrisch-Topologische Vorbereitungen.- 1 Beispiele für Räume, Abbildungen und topologische Probleme.- 2 Homotopie.- 3 Simplizialkomplexe und Polyeder.- 4 CW-Räume.- II Fundamentalgruppe und Überlagerungen.- 5 Die Fundamentalgruppe.- 6 Überlagerungen.- III Homologietheorie.- 7 Homologiegruppen von Simplizialkomplexen.- 8 Algebraische Hilfsmittel.- 9 Homologiegruppen topologischer Räume.- 10 Homologie mit Koeffizienten.- 11 Einige Anwendungen der Homologietheorie.- 12 Homologie von Produkten.- IV Cohomologie, Dualität und Produkte.- 13 Cohomologie.- 14 Dualität in Mannigfaltigkeiten.- 15 Der Cohomologiering.- V Fortsetzung der Homotopietheorie.- 16 Homotopiegruppen.- 17 Faserungen und Homotopiegruppen.- 18 Homotopieklassifikation von Abbildungen.- Symbole.Table of ContentsGeometrisch-Topologische Vorbereitungen: Beispiele für Räume, Abbildungen und topologische Probleme - Homotopie - Simplizialkomplexe und Polyeder - CW-Räume - Fundamentalgruppe und Überlagerungen: Die Fundamentalgruppe - Überlagerungen - Homologietheorie: Homologiegruppen von Simplizialkomplexen - Algebraische Hilfsmittel - Homologiegruppen topologischer Räume - Homologie mit Koeffizienten - Einige Anwendungen der Homologietheorie - Homologie von Produkten - Cohomologie, Dualität und Produkte: Cohomologie - Dualität in Mannigfaltigkeiten - Der Cohomologiering - Fortsetzung der Homotopietheorie: Homotopiegruppen - Faserungen und Homotopiegruppen - Homotopieklassifikation von Abbildungen
£31.34
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG A Groupoid Approach to C*-Algebras
Table of ContentsLocally compact groupoids.- The C*-algebra of a groupoid.- Some examples.
£24.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Categories in Continuum Physics: Lectures Given at a Workshop Held at SUNY, Buffalo 1982
Table of ContentsContinuum mechanics and geometric integration theory.- Structure of continuum physics.- On differentiable spaces.- Cartesian closed categories and analysis of smooth maps.- to synthetic differential geometry, and a synthetic theory of dislocations.- Synthetic reasoning and variable sets.- Recent research on the foundations of thermodynamics.- Global and local versions of the second law of thermodynamics.- Thermodynamics and the hahn-banach theorem.- What is the length of a potato?.
£24.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Cohomology of Sheaves
Book SynopsisThis 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.Table of ContentsI. 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.
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Equivariant K-Theory and Freeness of Group Actions on C*-Algebras
Book SynopsisFreeness of an action of a compact Lie group on a compact Hausdorff space is equivalent to a simple condition on the corresponding equivariant K-theory. This fact can be regarded as a theorem on actions on a commutative C*-algebra, namely the algebra of continuous complex-valued functions on the space. The successes of "noncommutative topology" suggest that one should try to generalize this result to actions on arbitrary C*-algebras. Lacking an appropriate definition of a free action on a C*-algebra, one is led instead to the study of actions satisfying conditions on equivariant K-theory - in the cases of spaces, simply freeness. The first third of this book is a detailed exposition of equivariant K-theory and KK-theory, assuming only a general knowledge of C*-algebras and some ordinary K-theory. It continues with the author's research on K-theoretic freeness of actions. It is shown that many properties of freeness generalize, while others do not, and that certain forms of K-theoretic freeness are related to other noncommutative measures of freeness, such as the Connes spectrum. The implications of K-theoretic freeness for actions on type I and AF algebras are also examined, and in these cases K-theoretic freeness is characterized analytically.Table of ContentsIntroduction: The commutative case.- Equivariant K-theory of C*-algebras.- to equivariant KK-theory.- Basic properties of K-freeness.- Subgroups.- Tensor products.- K-freeness, saturation, and the strong connes spectrum.- Type I algebras.- AF algebras.
£35.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Algebraic Cobordism
Book SynopsisFollowing Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. The book also contains some examples of computations and applications.Table of ContentsCobordism and oriented cohomology.- The definition of algebraic cobordism.- Fundamental properties of algebraic cobordism.- Algebraic cobordism and the Lazard ring.- Oriented Borel-Moore homology.- Functoriality.- The universality of algebraic cobordism.
£85.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Algebraic Topology - Homotopy and Homology
Book SynopsisFrom 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 Trade ReviewFrom the reviews: "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."R. Brown in Bulletin of the London Mathematical Society, 1980 "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)Table of Contentso. 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
£47.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Sheaves on Manifolds: With a Short History. «Les débuts de la théorie des faisceaux». By Christian Houzel
Book SynopsisSheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view. From the reviews: "Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." –Bulletin of the L.M.S.Table of ContentsA Short History: Les débuts de la théorie des faisceaux.- I. Homological algebra.- II. Sheaves.- III. Poincaré-Verdier duality and Fourier-Sato transformation.- IV. Specialization and microlocalization.- V. Micro-support of sheaves.- VI. Micro-support and microlocalization.- VII. Contact transformations and pure sheaves.- VIII. Constructible sheaves.- IX. Characteristic cycles.- X. Perverse sheaves.- XI. Applications to O-modules and D-modules.- Appendix: Symplectic geometry.- Summary.- A.1. Symplectic vector spaces.- A.2. Homogeneous symplectic manifolds.- A.3. Inertia index.- Exercises to the Appendix.- Notes.- List of notations and conventions.
£104.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG K-Theory: An Introduction
Book SynopsisFrom the Preface: K-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem. For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch considered a topological analog defined for any compact space X, a group K{X) constructed from the category of vector bundles on X. It is this ''topological K-theory" that this book will study. Topological K-theory has become an important tool in topology. Using K- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are S1, S3 and S7. Moreover, it is possible to derive a substantial part of stable homotopy theory from K-theory.The purpose of this book is to provide advanced students and mathematicians in other fields with the fundamental material in this subject. In addition, several applications of the type described above are included. In general we have tried to make this book self-contained, beginning with elementary concepts wherever possible; however, we assume that the reader is familiar with the basic definitions of homotopy theory: homotopy classes of maps and homotopy groups.Thus this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".Trade ReviewFrom the reviews: "Karoubi’s classic K-Theory, An Introduction … is ‘to provide advanced students and mathematicians in other fields with the fundamental material in this subject’. … K-Theory, An Introduction is a phenomenally attractive book: a fantastic introduction and then some. … serve as a fundamental reference and source of instruction for outsiders who would be fellow travelers." (Michael Berg, MAA Online, December, 2008)Table of ContentsVector Bundles.- First Notions of K-Theory.- Bott Periodicity.- Computation of Some K-Groups.- Some Applications of K-Theory.- Vector Bundles.- First Notions of K-Theory.- Bott Periodicity.- Computation of Some K-Groups.
£47.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Cyclic Homology
Book SynopsisFrom the reviews: "This is a very interesting book containing material for a comprehensive study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras and algebraic K-theory and an introduction to Connes'work and recent results on the Novikov conjecture. The book requires a knowledge of homological algebra and Lie algebra theory as well as basic technics coming from algebraic topology. The bibliographic comments at the end of each chapter offer good suggestions for further reading and research. The book can be strongly recommended to anybody interested in noncommutative geometry, contemporary algebraic topology and related topics." European Mathematical Society Newsletter In this second edition the authors have added a chapter 13 on MacLane (co)homology.Trade ReviewFrom the reviews: "This is a very interesting book containing material for a comprehensive study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras and algebraic K-theory and (in the last chapter) an introduction to Connes'work and recent results on the Novikov conjecture. The book requires a knowledge of homological algebra and Lie algebra theory as well as basic technics coTable of Contents1. Hochschild Homology.- 2. Cyclic Homology of Algebras.- 3. Smooth Algebras and Other Examples.- 4. Operations on Hochschild and Cyclic Homology.- 5. Variations on Cyclic Homology.- 6. The Cyclic Category, Tor and Ext Interpretation.- 7. Cyclic Spaces and Sl-Equivariant Homology.- 8. Chern Character.- 9. Classical Invariant Theory.- 10. Homology of Lie Algebras of Matrices.- 11. Algebraic K-Theory.- 12. Non-commutative Differential Geometry.- 13. Mac Lane (co)homology.- Appendices.- A. Hopf Algebras.- B. Simplicial.- C. Homology of Discrete Groups and Small Categories.- D. Spectral Sequences.- E. Smooth Algebras.- References.- References 1992–1996.- Symbols.
£104.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Algebraic Topology of Finite Topological Spaces and Applications
Book SynopsisThis volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen's conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.Trade ReviewFrom the reviews:“This book deals with the algebraic topology of finite topological spaces and its applications, and includes well-known results on finite spaces and original results developed by the author. The book is self-contained and well written. It is understandable and enjoyable to read. It contains a lot of examples and figures which help the readers to understand the theory.” (Fumihiro Ushitaki, Mathematical Reviews, March, 2014)“This book illustrates convincingly the idea that the study of finite non-Hausdorff spaces from a homotopical point of view is useful in many areas and can even be used to study well-known problems in classical algebraic topology. … This book is a revised version of the PhD Thesis of the author. … All the concepts introduced with the chapters are usefully illustrated by examples and the recollection of all these results gives a very nice introduction to a domain of growing interest.” (Etienne Fieux, Zentralblatt MATH, Vol. 1235, 2012)Table of Contents1 Preliminaries.- 2 Basic topological properties of finite spaces.- 3 Minimal finite models.- 4 Simple homotopy types and finite spaces.- 5 Strong homotopy types.- 6 Methods of reduction.- 7 h-regular complexes and quotients.- 8 Group actions and a conjecture of Quillen.- 9 Reduced lattices.- 10 Fixed points and the Lefschetz number.- 11 The Andrews-Curtis conjecture.
£32.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Algebraic Operads
Book SynopsisIn many areas of mathematics some “higher operations” are arising. These havebecome so important that several research projects refer to such expressions. Higher operationsform new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the Homotopy Transfer Theorem. Although the necessary notions of algebra are recalled, readers are expected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included. After a low-level chapter on Algebra, accessible to (advanced) undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers.Trade ReviewFrom the reviews:“It is a welcome addition to the existing literature and will, no doubt, become a standard reference for many authors working in this quickly developing field. … it is an impressive piece of work, which gives a comprehensive account of the foundations of the theory of algebraic operads, starting from the most basic notions, such as associative algebras and modules. It will be of interest to a broad swath of mathematicians: from undergraduate students to experts in the field.” (Andrey Yu. Lazarev, Mathematical Reviews, March, 2013)Table of ContentsPreface.- 1.Algebras, coalgebras, homology.- 2.Twisting morphisms.- 3.Koszul duality for associative algebras.- 4.Methods to prove Koszulity of an algebra.- 5.Algebraic operad.- 6 Operadic homological algebra.- 7.Koszul duality of operads.- 8.Methods to prove Koszulity of an operad.- 9.The operads As and A\infty.- 10.Homotopy operadic algebras.- 11.Bar and cobar construction of an algebra over an operad.- 12.(Co)homology of algebras over an operad.- 13.Examples of algebraic operads.- Apendices: A.The symmetric group.- B.Categories.- C.Trees.- References.- Index.- List of Notation.
£98.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Collected Papers - Gesammelte Abhandlungen
Book SynopsisFrom 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."Trade Review Heinz 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. Heinz 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. The 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. This book of over 1200 pages featuring 71 items constitutes an essential reference for the development of mathematics during the XXth century. Jean-Paul Pier (Zbl. MATH 980, 01027)Table of ContentsTable of Contents.- List of Publications of Heinz Hopf.- Editor's Preface.- Papers of Heinz Hopf.- Heinz Hopf Selecta.
£49.49
Springer Spektrum Topologie
Book Synopsis1 Logische Grundlagen für die Topologie.- 2 Elementare Topologie.- 3 Algebraische Grundlagen.- Teil I.- 4 Einstieg in die algebraische Topologie.- 5 Simpliziale Komplexe.- 6 Algebraische Grundlagen.- Teil II.- 7 Elemente der Homologietheorie.- 8 CW-Komplexe und einige ihrer Anwendungen.- 9 Algebraische Grundlagen.- Teil III.- 10 Kohomologie und die Poincaré-Dualität.- Literaturverzeichnis.- Index.
£31.34
Mathematical Society of Japan Singularity Theory And Its Application
Book SynopsisThis 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 AmericaTable of ContentsInvariants 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.
£84.60
Mathematical Society of Japan Finsler Geometry, Sapporo 2005 -- In Memory Of
Book SynopsisThe 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 AmericaTable of ContentsPart 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.
£56.05
Springer, India, Private Ltd Basic Algebraic Topology and its Applications
Book SynopsisThis 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.Focusing 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.Trade Review“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)“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)“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)Table of ContentsPrerequisite 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.
£89.99
Springer, India, Private Ltd Basic Algebraic Topology and its Applications
Book SynopsisThis 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.Focusing 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.Trade Review“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)“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)“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)Table of ContentsPrerequisite 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.
£62.99
Birkhauser Verlag AG Rigid Germs, the Valuative Tree, and Applications
Book SynopsisThis 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.The 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.In 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. In some cases, from such dynamical data one can construct special compact complex surfaces, called Kato surfaces, related to some conjectures in complex geometry.Table of ContentsIntroduction.-1.Background.- 2.Dynamics in 2D.- 3.Rigid germs in higher dimension.- 4 Construction of non-Kahler 3-folds.- References.- Index.
£13.29
Jainendra K Jain Algebraic Topology: A Primer
Book SynopsisThis 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.Table of Contents 1 Basic Topology: A review 2 The Fundamental Group 3 Simplicial Complexes 4 Simplicial Homology 5 Covering Projections 6 Singular Homology 7 Appendix References Index
£46.80
World Scientific Publishing Co Pte Ltd Quantum Topology
Book SynopsisThis book constitutes a review volume on the relatively new subject of Quantum Topology. Quantum Topology has its inception in the 1984/1985 discoveries of new invariants of knots and links (Jones, Homfly and Kauffman polynomials). These invariants were rapidly connected with quantum groups and methods in statistical mechanics. This was followed by Edward Witten's introduction of methods of quantum field theory into the subject and the formulation by Witten and Michael Atiyah of the concept of topological quantum field theories.This book is a review volume of on-going research activity. The papers derive from talks given at the Special Session on Knot and Topological Quantum Field Theory of the American Mathematical Society held at Dayton, Ohio in the fall of 1992. The book consists of a self-contained article by Kauffman, entitled Introduction to Quantum Topology and eighteen research articles by participants in the special session.This book should provide a useful source of ideas and results for anyone interested in the interface between topology and quantum field theory.
£108.00
World Scientific Publishing Co Pte Ltd Knots And Physics
Book SynopsisIn this second edition, the following recent papers have been added: “Gauss Codes, Quantum Groups and Ribbon Hopf Algebras”, “Spin Networks, Topology and Discrete Physics”, “Link Polynomials and a Graphical Calculus” and “Knots Tangles and Electrical Networks”. An appendix with a discussion on invariants of embedded graphs and Vassiliev invariants has also been included.This book is an introduction to knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of knot theory, coupled with a quantum statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems.Table of ContentsPhysical Knots; States and the Bracket Polynomial; The Jones Polynominal and Its Generalizations; Braids and Polynomials: Formal Feynman Diagrams, Bracket as Vacuum-Vacmum expectation and the Quantum Group SL(2)q; Yang-Baxter Models for Specialization's of the Homfly Polynomial; The Alexander Polynomial; Knot Crystals - Classical Knot Theory in Modem Guise; The Kauffman Polynomial; Three-Manifold Invariants from the Jones Polynomials; integral Heuristics and Witten's lnvariants; Chromatic Polynomials; The Potts Model and the Dichromatic Polynomial; The Penrose Theory of Spin Networks; Knots and Strings - Knotted Strings; DNA and Quantum Field Theory; Knots in Dynamical Systems - The Lorenz Attractor.
£90.90
World Scientific Publishing Co Pte Ltd Knots And Physics
Book SynopsisIn this second edition, the following recent papers have been added: “Gauss Codes, Quantum Groups and Ribbon Hopf Algebras”, “Spin Networks, Topology and Discrete Physics”, “Link Polynomials and a Graphical Calculus” and “Knots Tangles and Electrical Networks”. An appendix with a discussion on invariants of embedded graphs and Vassiliev invariants has also been included.This book is an introduction to knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of knot theory, coupled with a quantum statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems.Table of ContentsPhysical Knots; States and the Bracket Polynomial; The Jones Polynominal and Its Generalizations; Braids and Polynomials: Formal Feynman Diagrams, Bracket as Vacuum-Vacmum expectation and the Quantum Group SL(2)q; Yang-Baxter Models for Specialization's of the Homfly Polynomial; The Alexander Polynomial; Knot Crystals - Classical Knot Theory in Modem Guise; The Kauffman Polynomial; Three-Manifold Invariants from the Jones Polynomials; integral Heuristics and Witten's lnvariants; Chromatic Polynomials; The Potts Model and the Dichromatic Polynomial; The Penrose Theory of Spin Networks; Knots and Strings - Knotted Strings; DNA and Quantum Field Theory; Knots in Dynamical Systems - The Lorenz Attractor.
£35.15
World Scientific Publishing Co Pte Ltd Quantum Topology
Book SynopsisThis book constitutes a review volume on the relatively new subject of Quantum Topology. Quantum Topology has its inception in the 1984/1985 discoveries of new invariants of knots and links (Jones, Homfly and Kauffman polynomials). These invariants were rapidly connected with quantum groups and methods in statistical mechanics. This was followed by Edward Witten's introduction of methods of quantum field theory into the subject and the formulation by Witten and Michael Atiyah of the concept of topological quantum field theories.This book is a review volume of on-going research activity. The papers derive from talks given at the Special Session on Knot and Topological Quantum Field Theory of the American Mathematical Society held at Dayton, Ohio in the fall of 1992. The book consists of a self-contained article by Kauffman, entitled Introduction to Quantum Topology and eighteen research articles by participants in the special session.This book should provide a useful source of ideas and results for anyone interested in the interface between topology and quantum field theory.
£51.30
World Scientific Publishing Co Pte Ltd Lecture Notes On General Topology
Book SynopsisThis 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.Table of ContentsPreface; Introduction; Topological Spaces; Continuous Maps and Homeomorphisms; Connectedness; Separation Axioms and Quotient Axioms; Compactness; Product Spaces and Quotient Spaces; Appendix: Some Elementary Inequalities;
£49.50
World Scientific Publishing Co Pte Ltd Lectures On Algebraic Topology
Book SynopsisAlgebraic 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.
£112.50
World Scientific Publishing Co Pte Ltd Lectures On Algebraic Topology
Book SynopsisAlgebraic 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.
£49.50
World Scientific Publishing Company Collected Works of Anatole Katok The Volume I
Book Synopsis
£297.00
World Scientific Publishing Company Collected Works of Anatole Katok The Volume II
Book Synopsis
£297.00
World Scientific Publishing Co Pte Ltd Physical And Numerical Models In Knot Theory:
Book SynopsisThe 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.Table of ContentsPhysical Knot Theory: Universal Energy Spectrum of Tight Knots and Links in Physics (R Buniy & T Kephart); Three Knotty Ideas in Geometry: Pearl-Number, Ropelength and Rope Packing (R Kusner & 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 & 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.
£172.80
World Scientific Publishing Co Pte Ltd Topological Library - Part 2: Characteristic
Book SynopsisThis is the second of a three-volume set collecting the original and now-classic works in topology written during the 1950s-1960s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated “singular homologies of fiber spaces.”Table of ContentsOn Manifolds Homeomorphic to the 7-Sphere (J Milnor); Groups of Homotopy Spheres 1 (M A Kervaire & J Milnor); Homotopy Equivalent Smooth Manifolds (S P Novikov); Rational Pontrjagin Classes, Homeomorphism and Homotopy Type of Smooth Manifolds (S P Novikov); On Manifolds with Free Abelian Fundamental Group (S P Novikov); Stable Homeomorphisms and the Annulus Conjecture (R Kirby).
£118.80
Springer Verlag, Singapore Algebra 3: Homological Algebra and Its
Book SynopsisThis 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.Trade Review“This is an excellent book on Homological Algebra. All topics dealt here are presented in a very 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)Table of ContentsChapter 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.
£35.99
World Scientific Publishing Co Pte Ltd Braids: Introductory Lectures On Braids,
Book SynopsisThis book is an indispensable guide for anyone seeking to familarize themselves with research in braid groups, configuration spaces and their applications. Starting at the beginning, and assuming only basic topology and group theory, the volume's noted expositors take the reader through the fundamental theory and on to current research and applications in fields as varied as astrophysics, cryptography and robotics. As leading researchers themselves, the authors write enthusiastically about their topics, and include many striking illustrations. The chapters have their origins in tutorials given at a Summer School on Braids, at the National University of Singapore's Institute for Mathematical Sciences in June 2007, to an audience of more than thirty international graduate students.Table of ContentsTutorial on the Braid Groups; Simplicial Objects and Homotopy Groups; Introduction to Configuration Spaces and Their Applications; Braids and Magnetic Fields; Configuration Spaces, Braids, and Robotics; Braid Group Cryptography.
£117.00
World Scientific Publishing Co Pte Ltd Introductory Lectures On Knot Theory: Selected
Book SynopsisThis volume consists primarily of survey papers that evolved from the lectures given in the school portion of the meeting and selected papers from the conference.Knot theory is a very special topological subject: the classification of embeddings of a circle or collection of circles into three-dimensional space. This is a classical topological problem and a special case of the general placement problem: Understanding the embeddings of a space X in another space Y. There have been exciting new developments in the area of knot theory and 3-manifold topology in the last 25 years. From the Jones, Homflypt and Kauffman polynomials, quantum invariants of 3-manifolds, through, Vassiliev invariants, topological quantum field theories, to relations with gauge theory type invariants in 4-dimensional topology.More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.It is a remarkable fact that knot theory, while very special in its problematic form, involves ideas and techniques that involve and inform much of mathematics and theoretical physics. The subject has significant applications and relations with biology, physics, combinatorics, algebra and the theory of computation. The summer school on which this book is based contained excellent lectures on the many aspects of applications of knot theory. This book gives an in-depth survey of the state of the art of present day knot theory and its applications.
£153.00
World Scientific Publishing Co Pte Ltd Morse Theory Of Gradient Flows, Concavity And
Book SynopsisThis monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical structures and constructions in the book fit comfortably in the framework of Morse Theory and, more generally, of the Singularity Theory of smooth maps.The geometric and combinatorial structures, arising from the interactions of vector flows with the boundary of the manifold, are surprisingly rich. This geometric setting leads organically to many encounters with Singularity Theory, Combinatorics, Differential Topology, Differential Geometry, Dynamical Systems, and especially with the boundary value problems for ordinary differential equations. This diversity of connections animates the book and is the main motivation behind it.The book is divided into two parts. The first part describes the flows in three dimensions. It is more pictorial in nature. The second part deals with the multi-dimensional flows, and thus is more analytical. Each of the nine chapters starts with a description of its purpose and main results. This organization provides the reader with independent entrances into different chapters.Table of ContentsPart I: Flows and Spines on 3-manifolds; Vector Fields, Morse Stratifications, and Gradient Spines of 3-folds; Combinatorial and Gradient Complexities of 3-folds; Flow Deformations and Gradient Spines in 3D; Part II: Morse Theory on Manifolds with Boundary; Morse Stratifications and Tangency of Vector Fields to the Boundary; Spaces of Multi-tangent Trajectories; Spines and Flow Spines; Schwartz Genera as a Complexity Measure of Traversing Flows; Spectral Sequences for Spaces of Multi-tangent Trajectories and the Filtration Invariants of Flows; Convexly Enveloped Bordisms of Morse Data and the Complements to Discriminants of Smooth Maps; The Burnside-ring-valued Morse Formula for Vector Fields on Manifolds with Boundary.
£153.00
World Scientific Publishing Co Pte Ltd Excursion In Diagrammatic Algebra, An: Turning A
Book SynopsisThe aim of this book is to give as detailed a description as is possible of one of the most beautiful and complicated examples in low-dimensional topology. This example is a gateway to a new idea of higher dimensional algebra in which diagrams replace algebraic expressions and relationships between diagrams represent algebraic relations. The reader may examine the changes in the illustrations in a leisurely fashion; or with scrutiny, the reader will become familiar and develop a facility for these diagrammatic computations.The text describes the essential topological ideas through metaphors that are experienced in everyday life: shadows, the human form, the intersections between walls, and the creases in a shirt or a pair of trousers. Mathematically informed reader will benefit from the informal introduction of ideas. This volume will also appeal to scientifically literate individuals who appreciate mathematical beauty.Table of ContentsA Sphere; Surfaces, Folds, and Cusps; The Inside and Outside; Dimensions; Immersed Surfaces; Movies; Movie Moves; Taxonomic Summary; How Not to Turn the Sphere Inside-Out; A Physical Metaphor; Sarah's Thesis; The Eversion; The Double Point and Fold Surfaces.
£86.40
World Scientific Publishing Co Pte Ltd Knots And Physics (Fourth Edition)
Book SynopsisThis invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas.The book is divided into two parts: Part I is a systematic course on knots and physics starting from the ground up, and Part II is a set of lectures on various topics related to Part I. Part II includes topics such as frictional properties of knots, relations with combinatorics, and knots in dynamical systems.In this new edition, an article on Virtual Knot Theory and Khovanov Homology has beed added.Table of ContentsPhysical Knots; States and the Bracket Polynomial; The Jones Polynomial and Its Generalizations; Braids and the Jones Polynomial; Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)q; Yang - Baxter Models for Specializations of the Homfly Polynomial; Knot-Crystals - Classical Knot Theory in a Modern Guise; The Kauffman Polynomial; Three Manifold Invariants from the Jones Polynomial; Integral Heuristics and Witten's Invariants; The Chromatic Polynomial; The Potts Model and the Dichromatic Polynomial; The Penrose Theory of Spin Networks; Knots and Strings - Knotted Strings; DNA and Quantum Field Theory; Knots in Dynamical Systems - The Lorenz Attractor; and selected papers.
£247.50
