Topology Books
Springer New York An Introduction To Semiclassical And Microlocal Analysis Hb
Book SynopsisThis book presents the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics in a pedagogical, way and is mainly addressed to non-specialists in the subject.Trade ReviewFrom the reviews: "The book is very clearly written, and is indeed much simpler than most of others. … this is an excellent book, suitable even for students with a poor background in the subject. In my opinion, every department offering courses on partial differential equations or asymptotic analysis should have it in the library. It will be very useful to all mathematicians working in semi-classical or microlocal analysis … ." (Yuri Safarov, Bulletin of the London Mathematical Society, Issue 35, 2003) "This is a concise and accessible book on the basic techniques of semiclassical and microlocal analysis. … An appendix provides a useful summary of the major formulas used in the text. Each chapter is followed by a collection of provocative and well chosen exercises. The exercises are essential for understanding the work and provide important applications. … the text does provide a very readable, clear, and concise introduction to semiclassical and microlocal analysis." (Peter D. Hislop, Mathematical Reviews, 2003 b) "The contents of the book correspond to a course at Ph. D. Level, given by the author at the Universities of Bologna and Paris-Nord. … the book collects in an original way standard results and new aspects of semi-classical microlocal analysis; the reading is suggested to non-specialists as well." (L. Rodino, Zentralblatt MATH, Vol. 994 (19), 2002) "This book presents most of the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics. … The originality lies in the fact that the main features of analytic microlocal analysis are derived from a single and elementary a priori estimate. Various exercises illustrate the chief results of each chapter while introducing the reader to further developments of the theory. Applications to the study of the Schrödinger operator are also discussed, to further the understanding of new notions … ." (L’ Enseignement Mathematique, Vol. 48 (1-2), 2002) "The book under review consists of lecture notes corresponding to a course taught for several years at the universities of Paris-Nord (France) and Bologna (Italy). It is addressed mainly to non-specialists in the subject, and the prerequisites are essentially reduced to the basic notions of the theory of distributions. … The author tries to make clear how the things work and show examples where they can be applied. It is nicely written … . the book can be highly recommended." (J. Synnatzschke, Zeitschrift für Analysis und ihre Anwendungen – ZAA, Vol. 21 (3), 2002)Table of ContentsIntroduction * Semiclassical Pseudodifferential Calculus * Microlocalization * Applications to the Solutions of Analytic Linear PDEs * Complements: Symplectic Aspects * Appendix: List of Formulae * Bibliography * Index * List of Notations
£71.24
Springer-Verlag New York Inc. Introduction to Mechanics and Symmetry
Book SynopsisSpecific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering.Trade Review"The book is self-contained.It remains a good and solid introduction to this subject."Nieuw Archief voor Wiskunde, March 2001 "... This book takes the reader on one of the greatest journeys in modern mathematics that has as its roots a subject that is more than 300 years old. Armed with this knowledge a reader is ready to pursue numerous topics of active mathematical research, from the more pure domains of symplectic geometry and topology to the geometric analysis of the limitless supply of examples from mechanics."Newsletter of the Newzealand Mathematical Society, No. 81, April 2001 Second Edition J.E. Marsden and T.S. Ratiu Introduction to Mechanics and Symmetry A Basic Exposition of Classical Mechanical Systems "As the name of the book implies, a consistent theme running through the book is that of symmetry. Indeed the latter half of the book focuses on Poisson manifolds, momentum maps, Lie-Poisson reduction, co-adjoint orbits and the integrability of the rigid body. The discussion of reduction must be the most comprehensive yet given. A pleasant feature of the book is that most of the theory that relates to finite-dimensional mechanical systems is illustrated concretely in terms of local coordinates, thereby making the book accessible even to beginners in the field."—MATHEMATICAL REVIEWSTable of ContentsPreface * About the Authors * 1 Introduction and Overview * 2 Hamiltonian Systems on Linear Symplectic Spaces * 3 An Introduction to Infinite-Dimensional Systems * 4 Manifolds, Vector Fields, and Differential Forms * 5 Hamiltonian Systems on Symplectic Manifolds * 6 Cotangent Bundles * 7 Lagrangian Mechanics * 8 Variational Principles, Constraints, and Rotating Systems * 9 An Introduction to Lie Groups * 10 Poisson Manifolds * 11 Momentum Maps *12 Computation and Properties of Momentum Maps * 13 Lie-Poisson and Euler-Poincare Reduction * 14 Coadjoint Orbits * 15 The Free Rigid Body * References
£67.49
Elsevier Science Recent Progress in General Topology II
£140.00
Penguin Publishing Group Poincares Prize The HundredYear Quest to Solve One of Maths Greatest Puzzles
Book SynopsisThe amazing story of one of the greatest math problems of all time and the reclusive genius who solved itIn the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found.Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.
£16.97
John Wiley & Sons Inc Geometry by Discovery
Book SynopsisThis text seeks to get students actively involved in problem-solving, especially of a geometric nature. The approach highlights the mathematical connections between concepts, and aims to enhance students' geometrical intuition.Table of ContentsGetting Started: Strategies for Solving Problems. Episodes in the Measurement of Length, Area, and Volume. Polyhedra. Shortest Path Problems. Kaleidoscopes. Symmetry. What Shapes Are Best? Beehives and Other Packing Problems. Where to Go From Here?: Project Ideas. Credits. Index.
£179.06
John Wiley & Sons Inc Methods of Geometry
Book SynopsisExceptionally well-written, with engaging historical and bibliographic notes, Methods of Geometry sets serious competition to similar titles in the field. It downplays the theory while emphasizing a practical, accessible, proof-oriented approach.Trade Review"It should be emphasized that the book is filled with historicaland bibliographic notes, good motivations and a number ofexercises. Altogether, it can be regarded as a good approach to aspecial part of geometry on an intermediate level." (ZentralblattMath, Volume 955, No 5, 2001) "Fine interweaving of history, foundations, and geometry.... Usefulas a source of exercises." (American Mathematical Monthly, November2001)Table of ContentsFoundations. Elementary Euclidean Geometry. Exercises on Elementary Geometry. Some Triangle and Circle Geometry. Plane Isometries and Similarities. Three Dimensional Isometries and Similarities. Symmetry. Appendices. Bibliography. Index.
£147.56
John Wiley & Sons Inc An Introduction to Metric Spaces and Fixed Point
Book SynopsisThis book provides an excellent introduction to the subject designed for readers from a variety of mathematical backgrounds. It features introductory properties of metric spaces and Banach spaces, and an appendix contains a summary of the concepts of set theory.Trade Review"...deserves to be on the bookshelf of everyone who wants to know about fixed-point theory in metric and Banach spaces and experts who want to read an insightful survey of some basic ideas..." (Mathematical Reviews, 2002b) "Clear, friendly exposition." (American Mathematical Monthly, August/September 2002)Table of ContentsPreface ix I Metric Spaces 1 Introduction 3 1.1 The real numbers R 3 1.2 Continuous mappings in R 5 1.3 The triangle inequality in R 7 1.4 The triangle inequality in R" 8 1.5 Brouwer's Fixed Point Theorem 10 Exercises 11 2 Metric Spaces 13 2.1 The metric topology 15 2.2 Examples of metric spaces 19 2.3 Completeness 26 2.4 Separability and connectedness 33 2.5 Metric convexity and convexity structures 35 Exercises 38 3 Metric Contraction Principles 41 3.1 Banach's Contraction Principle 41 3.2 Further extensions of Banach's Principle 46 3.3 The Caristi-Ekeland Principle 55 3.4 Equivalents of the Caristi-Ekeland Principle 58 3.5 Set-valued contractions 61 3.6 Generalized contractions 64 Exercises 67 4 Hyperconvex Spaces 71 4.1 Introduction 71 4.2 Hyperconvexity 77 4.3 Properties of hyperconvex spaces 80 4.4 A fixed point theorem 84 4.5 Intersections of hyperconvex spaces 87 4.6 Approximate fixed points 89 4.7 Isbell's hyperconvex hull 91 Exercises 98 5 "Normal" Structures in Metric Spaces 101 5.1 A fixed point theorem 101 5.2 Structure of the fixed point set 103 5.3 Uniform normal structure 106 5.4 Uniform relative normal structure 110 5.5 Quasi-normal structure 112 5.6 Stability and normal structure 115 5.7 Ultrametric spaces 116 5.8 Fixed point set structure—separable case 120 Exercises 123 II Banach Spaces 6 Banach Spaces: Introduction 127 6.1 The definition 127 6.2 Convexity 131 6.3 £2 revisited 132 6.4 The modulus of convexity 136 6.5 Uniform convexity of the tp spaces 138 6.6 The dual space: Hahn-Banach Theorem 142 6.7 The weak and weak* topologies 144 6.8 The spaces c, CQ, t\ and ^ 146 6.9 Some more general facts 148 6.10 The Schur property and £j 150 6.11 More on Schauder bases in Banach spaces 154 6.12 Uniform convexity and reflexivity 163 6.13 Banach lattices 165 Exercises 168 7 Continuous Mappings in Banach Spaces 171 7.1 Introduction 171 7.2 Brouwer's Theorem 173 7.3 Further comments on Brouwer's Theorem 176 7.4 Schauder's Theorem 179 7.5 Stability of Schauder's Theorem 180 7.6 Banach algebras: Stone Weierstrass Theorem 182 7.7 Leray-Schauder degree 183 7.8 Condensing mappings 187 7.9 Continuous mappings in hyperconvex spaces 191 Exercises 195 8 Metric Fixed Point Theory 197 8.1 Contraction mappings 197 8.2 Basic theorems for nonexpansive mappings 199 8.3 A closer look at ßë 205 8.4 Stability results in arbitrary spaces 207 8.5 The Goebel-Karlovitz Lemma 211 8.6 Orthogonal convexity 213 8.7 Structure of the fixed point set 215 8.8 Asymptotically regular mappings 219 8.9 Set-valued mappings 222 8.10 Fixed point theory in Banach lattices 225 Exercises 238 9 Banach Space Ultrapowers 243 9.1 Finite representability 243 9.2 Convergence of ultranets 248 9.3 The Banach space ultrapower X 249 9.4 Some properties of X 252 9.5 Extending mappings to X 255 9.6 Some fixed point theorems 257 9.7 Asymptotically nonexpansive mappings 262 9.8 The demiclosedness principle 263 9.9 Uniformly non-creasy spaces 264 Exercises 270 Appendix: Set Theory 273 A.l Mappings 273 A.2 Order relations and Zermelo's Theorem 274 A.3 Zorn's Lemma and the Axiom Of Choice 275 A.4 Nets and subnets 277 A.5 Tychonoff's Theorem 278 A.6 Cardinal numbers 280 A. 7 Ordinal numbers and transfinite induction 281 A.8 Zermelo's Fixed Point Theorem 284 A.9 A remark about constructive mathematics 286 Exercises 287 Bibliography 289 Index 301
£157.45
John Wiley & Sons Inc Introduction to Geometry
Book SynopsisThis classic work is now available in an unabridged paperback edition. The Second Edition retains all the characterisitcs that made the first edition so popular: brilliant exposition, the flexibility permitted by relatively self-contained chapters, and broad coverage ranging from topics in the Euclidean plane, to affine geometry, projective geometry, differential geometry, and topology. The Second Edition incorporates improvements in the text and in some proofs, takes note of the solution of the 4-color map problem, and provides answers to most of the exercises.Table of ContentsPart I Triangles 3 Regular Polygons 26 Isometry in the Euclidean Plane 39 Two-Dimensional Crystallography 50 Similarity in the Euclidean Plane 67 Circles and Spheres 77 Isometry and Similarity in Euclidean Space 96 Part II Coordinates 107 Complex Numbers 135 The Five Platonic Solids 148 The Golden Section and Phyllotaxis 160 Part III Ordered Geometry 175 Affine Geometry 191 Projective Geometry 229 Absolute Geometry 263 Hyperbolic Geometry 287 Part IV Differential Geometry of Curves 307 The Tensor Notation 328 Differential Geometry of Surfaces 342 Geodesics 366 Topology of Surfaces 379 Four-Dimensional Geometry 396 Tables 413 References 415 Answers to Exercises 419 Index 459
£146.66
John Wiley & Sons Inc Combinatorial Geometry
Book SynopsisA complete, self-contained introduction to a powerful and resurging mathematical discipline. Combinatorial Geometry presents and explains with complete proofs some of the most important results and methods of this relatively young mathematical discipline, started by Minkowski, Fejes Toth, Rogers, and Erd???s.Table of ContentsARRANGEMENTS OF CONVEX SETS. Geometry of Numbers. Approximation of a Convex Set by Polygons. Packing and Covering with Congruent Convex Discs. Lattice Packing and Lattice Covering. The Method of Cell Decomposition. Methods of Blichfeldt and Rogers. Efficient Random Arrangements. Circle Packings and Planar Graphs. ARRANGEMENTS OF POINTS AND LINES. Extremal Graph Theory. Repeated Distances in Space. Arrangement of Lines. Applications of the Bounds on Incidences. More on Repeated Distances. Geometric Graphs. Epsilon Nets and Transversals of Hypergraphs. Geometric Discrepancy. Hints to Exercises. Bibliography. Indexes.
£155.66
John Wiley & Sons Inc Fundamentals of Three Dimensional Descriptive
Book SynopsisA complete overview of the fundamentals of three-dimensional descriptive geometry From an overview of the history of descriptive geometry to the application of the principles of descriptive geometry to real-world scenarios, Fundamentals of Three-Dimensional Descriptive Geometry provides a comprehensive look at the topic. Used throughout the disciplines of science, engineering, and architecture, descriptive geometry is crucial for everything from understanding the various segments and inter-workings of structural systems to grasping the relationship of molecules in a chemical compound. For those requiring a full accounting of the fundamentals of three-dimensional descriptive geometry, this text is a definitive and comprehensive resource.Table of ContentsPrinciples and Basic Concepts of Three-Dimensional DescriptiveGeometry. Lines in a Three-Dimensional Space. Plane Surfaces in a Three-Dimensional Space. Three-Dimensional Spatial Relationships of Lines and Planes. Rotation of Geometric Elements in a Three-Dimensional Space. Location of Points and Tangent Planes on Geometric Solids andSurfaces. Intersections of Common Geometric Solids and Surfaces. Development of Surfaces of Basic Geometric Solids. Principles of Descriptive Geometry Applied to Three-DimensionalSpace Vectors. Principles of Descriptive Geometry Applied to SelectedTopics. Principles of Descriptive Geometry Applied to Practical Problems.
£204.26
John Wiley & Sons Inc Fractals Random Shapes and Point Fields
Book SynopsisIn Part I the reader is introduced to the methods of measuring the fractal dimension of irregular geometric structures. Part II demonstrates important modern methods for the statistical analysis of random shapes. The statistical theory of point fields, with and without marks, is introduced in Part III. Each of the three sections concentrates on the mathematical ideas, rather than detailed proofs, and can be read independently.Table of ContentsFRACTALS AND METHODS FOR THE DETERMINATION OF FRACTALDIMENSIONS. Hausdorff Measure and Dimension. Deterministic Fractals. Random Fractals. Methods for the Empirical Determination of Fractal Dimension. THE STATISTICS OF SHAPES AND FORMS. Fundamental Concepts. Representation of Contours. Set Theoretic Analysis. Point Description of Figures. Examples. POINT FIELD STATISTICS. Fundamentals. Finite Point Fields. Poisson Point Fields. Fundamentals of the Theory of Point Fields. Statistics for Homogeneous Point Fields. Point Field Models. Appendices. References. Index.
£209.66
John Wiley & Sons Inc Techniques in Fractal Geometry
Book SynopsisFollowing on from the success of Fractal Geometry: Mathematical Foundations and Applications, this new sequel presents a variety of techniques in current use for studying the mathematics of fractals. Much of the material presented in this book has come to the fore in recent years.Table of ContentsMathematical Background. Review of Fractal Geometry. Some Techniques for Studying Dimension. Cookie-cutters and Bounded Distortion. The Thermodynamic Formalism. The Ergodic Theorem and Fractals. The Renewal Theorem and Fractals. Martingales and Fractals. Tangent Measures. Dimensions of Measures. Some Multifractal Analysis. Fractals and Differential Equations. References. Index.
£99.86
Dover Publications Introduction to Topology
Book SynopsisThis volume explains nontrivial applications of metric space topology to analysis, clearly establishing their relationship. Also, topics from elementary algebraic topology focus on concrete results with minimal algebraic formalism. Two chapters consider metric space and point-set topology; the other 2 chapters discuss algebraic topological material. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
£15.29
Dover Publications Inc. Croom F Principles of Topology
Book SynopsisDesigned for a one-semester introduction to topology at the undergraduate and beginning graduate levels, this text is accessible to students who have studied multivariate calculus. Topics include metric spaces, general topological spaces, continuity, topological equivalence, basis and subbasis, connectedness and compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces.
£18.69
Dover Publications Inc. Introduction to Topological Groups
Book SynopsisAfter an introductory chapter on the fundamentals of topology and group theory, this book presents a concise treatment of several more advanced subjects. Topics include semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras.
£14.39
Dover Publications Inc. General Topology
Book Synopsis
£16.14
Cambridge University Press Topology via Logic
Book SynopsisThis is an advanced textbook on topology for computer scientists. It is based on a course given by the author to postgraduate students of computer science at Imperial College.Table of Contents1. Introduction; 2. Affirmative and refutative assertions; 3. Frames; 4. Frames as algebras; 5. Topology: the definitions; 6. New topologies for old; 7. Point logic; 8. Compactness; 9. Spectral algebraic locales; 10. Domain theory; 11. Power domains; 12. Spectra of rings; Bibliography.
£47.99
Cambridge University Press Geometry and Topology
Book SynopsisGeometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. This book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate changes that generate symmetries. The discussion moves from Euclidean to non-Euclidean geometries, including spherical and hyperbolic geometry, and then on to affine and projective linear geometries. Group theory is introduced to treat geometric symmetries, leading to the unification of geometry and group theory in the Erlangen program. An introduction to basic topology follows, with the MÃbius strip, the Klein bottle and the surface with g handles exemplifying quotient topologies and the homeomorphism problem. Topology combines with group theory to yield the geometry of transformation groups,having applications to relativity theory and quantum mechTrade ReviewA welcome addition to the undergraduate library. Highly recommended. --ChoiceTable of ContentsIntroduction; 1. Euclidean geometry; 2. Composing maps; 3. Non-Euclidean; 4. Affine geometry; 5. Projective geometry; 6. Geometry and group theory; 7. Topology; 8. Geometry of transformation groups; 9. Concluding remarks; A. Metrics; B. Linear algebra; References; Index.
£49.39
Cambridge University Press When Topology Meets Chemistry
Book SynopsisIn this topology text, the reader will learn about knot theory, 3-dimensional manifolds, and the topology of embedded graphs, and the role these play in understanding molecular structures. All the relevant background is provided. For advanced undergraduate mathematics students, and researchers in chemistry and biology.Trade Review'If you are a chemist … looking for applications of low dimensional topology in the natural sciences, this is a book you should own … serves as an excellent introduction to the field for a topologist looking for interesting applications of topology in science. The book is well produced with many useful diagrams and with exercises that range from easy to intriguing. This book is definitely on my 'buy list'.' Stuart Whittington, SIAM ReviewTable of Contents1. Stereochemical topology; 2. Detecting chirality; 3. Chiral moebius ladders and related molecular graphs; 4. Different types of chirality and achirality; 5. Embeddings of complete graphs in 3-space; 6. Rigid and non-rigid symmetries of graphs in 3-space; 7. Topology of DNA.
£34.99
Cambridge University Press Lectures on the Ricci Flow 325 London Mathematical Society Lecture Note Series Series Number 325
Book SynopsisHamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the Poincaré conjecture and Thurston's geometrization conjecture. This book gives a concise introduction to the subject with the hindsight of Perelman's breakthroughs from 2002/2003.Trade Review"... The freedom to skip some of the proofs, and the lucid presentation, this small book is pleasant to read." Peng Lu, Mathematical ReviewsTable of Contents1. Introduction; 2. Riemannian geometry background; 3. The maximum principle; 4. Comments on existence theory for parabolic PDE; 5. Existence theory for the Ricci flow; 6. Ricci flow as a gradient flow; 7. Compactness of Riemannian manifolds and flows; 8. Perelman's W entropy functional; 9. Curvature pinching and preserved curvature properties under Ricci flow; 10. Three-manifolds with positive Ricci curvature and beyond.
£61.19
Cambridge University Press Frobenius Manifolds and Moduli Spaces for Singularities 151 Cambridge Tracts in Mathematics Series Number 151
Book SynopsisThe relations between Frobenius manifolds and singularity theory are treated here in a rigorous yet accessible manner. For those working in singularity theory or other areas of complex geometry, this book will open the door to the study of Frobenius manifolds. This class of manifolds are now known to be relevant for the study of singularity theory, quantum cohomology, mirror symmetry, symplectic geometry and integrable systems. The first part of the book explains the theory of manifolds with a multiplication on the tangent bundle. The second presents a simplified explanation of the role of Frobenius manifolds in singularity theory along with all the necessary tools and several applications. Readers will find here a careful and sound study of the fundamental structures and results in this exciting branch of maths. This book will serve as an excellent resource for researchers and graduate students who wish to work in this area.Trade Review'… a nice introduction to the theory of Frobenius manifolds …' Zentralblatt für Mathematik'The book under review gives a very detailed analysis of the category of F-manifolds … the book is clean, rigorous and readable. the researchers in the areas of singularity theory, complex geometry, integrable systems, quantum cohomology, mirror symmetry and sympathetic geometry will find in this book a lot of useful information which has never been given in such detail before.' Proceedings of the Edinburgh Mathematical Society'… one can say this book is a must for workers in the field of singularity theory.' Duco van Straten, Department of Mathematics, University of MainzTable of ContentsPart I. Multiplication on the Tangent Bundle: 1. Introduction to part 1; 2. Definition and first properties of F-manifolds; 3. Massive F-manifolds and Lagrange maps; 4. Discriminants and modality of F-manifolds; 5. Singularities and Coxeter groups; Part II. Frobenius Manifolds, Gauss-Manin Connections, and Moduli Spaces for Hypersurface Singularities: 6. Introduction to part 2; 7. Connections on the punctured plane; 8. Meromorphic connections; 9. Frobenius manifolds ad second structure connections; 10. Gauss-Manin connections for hypersurface singularities; 11. Frobenius manifolds for hypersurface singularities; 12. ∴μυ-constant stratum; 13. Moduli spaces for singularities; 14. Variance of the spectral numbers.
£105.45
Cambridge University Press The Life of Bach Musical Lives
Book SynopsisArising from a summer school course, this book develops the modern theory of rational varieties at a level that will particularly suit graduate students. The authors have written a state-of-the-art treatment with numerous exercises and solutions to help students reach the stage where they can begin to tackle contemporary research.Trade Review'… a beautiful and ample introduction to the interesting topic of rational and 'nearly rational' varieties and it will be a valuable reference for a wide audience.' Zentralblatt MATHTable of ContentsIntroduction; 1. Examples of rational varieties; 2. Cubic surfaces; 3. Rational surfaces; 4. Nonrationality and reduction modulo p; 5. The Noether-Fano method; 6. Singularities of pairs; 7. Solutions to exercises.
£105.45
Cambridge University Press The CubeA Window to Convex and Discrete Geometry
Book SynopsisThis tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them.Trade Review"Because this book is a love letter to the unity of mathematics, readers can hardly but come to share Zong's undisguised enthusiasm...Highly recommended." -- ChoiceTable of ContentsPreface; Basic notation; 0. Introduction; 1. Cross sections; 2. Projections; 3. Inscribed simplices; 4. Triangulations; 5. 0/1 polytopes; 6. Minkowski's conjecture; 7. Furtwangler's conjecture; 8. Keller's conjecture; Bibliography; Index.
£105.45
Cambridge University Press An Introduction to Contact Topology 109 Cambridge
Book SynopsisThis text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.Trade Review'… a fundamental monograph … can be strongly recommended for graduate students and is indispensable for specialists in the field.' EMS NewsletterTable of ContentsForeword; 1. Facets of Contact Geometry; 2. Contact Manifolds; 3. Knots in Contact 3-Manifolds; 4. Contact Structures on 3-Manifolds; 5. Symplectic Fillings and Convexity; 6. Contact Surgery; 7. Further Constructions of Contact Manifolds; 8. Contact Structures on 5-Manifolds; Appendix A. The generalised Poincaré lemma; Appendix B. Time-dependent vector fields; References; Notation Index; Author Index; Subject Index.
£77.89
Cambridge University Press Kazhdans Property T 11 New Mathematical Monographs Series Number 11
Book SynopsisProperty (T) is a rigidity property for topological groups, first formulated by D. Kazhdan in the mid 1960's with the aim of demonstrating that a large class of lattices are finitely generated. Later developments have shown that Property (T) plays an important role in an amazingly large variety of subjects, including discrete subgroups of Lie groups, ergodic theory, random walks, operator algebras, combinatorics, and theoretical computer science. This monograph offers a comprehensive introduction to the theory. It describes the two most important points of view on Property (T): the first uses a unitary group representation approach, and the second a fixed point property for affine isometric actions. Via these the authors discuss a range of important examples and applications to several domains of mathematics. A detailed appendix provides a systematic exposition of parts of the theory of group representations that are used to formulate and develop Property (T).Table of ContentsIntroduction; Part I. Kazhdan's Property (T): 1. Property (T); 2. Property (FH); 3. Reduced Cohomology; 4. Bounded generation; 5. A spectral criterion for Property (T); 6. Some applications of Property (T); 7. A short list of open questions; Part II. Background on Unitary Representations: A. Unitary group representations; B. Measures on homogeneous spaces; C. Functions of positive type; D. Representations of abelian groups; E. Induced representations; F. Weak containment and Fell topology; G. Amenability; Appendix; Bibliography; List of symbols; Index.
£133.95
Princeton University Press Combinatorics of Train Tracks
Book SynopsisMeasured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in two-and three-dimensional topology, geometry, and dynamical systems. This book presents a treatment of the combinatorial structure of the space of measured geodesic laminations in a fixed surface.Trade Review"The book is beautifully written, with a clear path of theoretical development amid a wealth of detail for the technician... [T]his text provides a valuable reference work as well as a readable introduction for the student or newcomer to the area."--Zentralblatt for MathematikTable of ContentsPrefaceAcknowledgementsCh. 1The Basic Theory31.1Train Tracks41.2Multiple Curves and Dehn's Theorem101.3Recurrence and Transverse Recurrence181.4Genericity and Transverse Recurrence391.5Trainpaths and Transverse Recurrence601.6Laminations681.7Measured Laminations821.8Bounded Surfaces and Tracks with Stops102Ch. 2Combinatorial Equivalence1152.1Splitting, Shifting, and Carrying1162.2Equivalence of Birecurrent Train Tracks1242.3Splitting versus Shifting1272.4Equivalence versus Carrying1332.5Splitting and Efficiency1392.6The Standard Models1452.7Existence of the Standard Models1542.8Uniqueness of the Standard Models160Ch. 3The Structure of ML[subscript 0]1733.1The Topology of ML[subscript 0] and PL[subscript 0]1743.2The Symplectic Structure of ML[subscript 0]1823.3Topological Equivalence1883.4Duality and Tangential Coordinates191Epilogue204Addendum The Action of Mapping Classes on ML[subscript 0]210Bibliography214
£70.40
Princeton University Press ThreeDimensional Geometry and Topology Volume 1
Book SynopsisHyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning, but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book develops some of the power of geometry in two and three dimensions, and the strong connection of geometry with topology.Trade ReviewWinner of the 2005 Book Prize, American Mathematical Society Winner of the 1997 for the Best Professional/Scholarly Book in Mathematics, Association of American Publishers "The present volume represents the culmination of nearly two decades of honoring his famous but difficult 1978 lecture notes. This beautifully produced, exquisitely organized volume now reads as easily as one could possibly hope given the profundity of the material. An instant classic."--ChoiceTable of ContentsPreface Reader's Advisory Ch. 1. What Is a Manifold? 3 Ch. 2. Hyperbolic Geometry and Its Friends 43 Ch. 3. Geometric Manifolds 109 Ch. 4. The Structure of Discrete Groups 209 Glossary 289 Bibliography 295 Index 301
£84.00
Princeton University Press Combinatorial Group Theory and Topology
Book SynopsisTable of Contents*Frontmatter, pg. i*CONTENTS, pg. v*PREFACE, pg. vii*PROBLEMS IN COMBINATORIAL GROUP THEORY, pg. 3*POINCARE DUALITY GROUPS OF DIMENSION TWO ARE SURFACE GROUPS, pg. 35*HOW TO GENERALIZE ONE-RELATOR GROUP THEORY, pg. 53*GRAPHICAL THEORY OF AUTOMORPHISMS OF FREE GROUPS, pg. 79*PEAK REDUCTION AND AUTOMORPHISMS OF FREE GROUPS AND FREE PRODUCTS, pg. 107*NONSINGULAR EQUATIONS OF SMALL WEIGHT OVER GROUPS, pg. 121*GRAPH-THEORETIC LEMMA AND GROUP-EMBEDDINGS, pg. 145*THE TODD-COXETER PROCESS, USING GRAPHS, pg. 157*A SUBGROUP THEOREM FOR PREGROUPS, pg. 163*GROUPS WITH A RATIONAL CROSS-SECTION, pg. 175*ON THE RATIONAL GROWTH OF VIRTUALLY NILPOTENT GROUPS, pg. 185*SJOGREN'S THEOREM FOR DIMENSION SUBGROUPS - THE METABELIAN CASE, pg. 197*ON GROUP PRESENTATIONS, COPRODUCTS AND INVERSES, pg. 213*ON COMPLEXES DOMINATED BY A TWO-COMPLEX, pg. 221*SUBCOMPLEXES OF TWO-COMPLEXES AND PROJECTIVE CROSSED MODULES, pg. 255*LENGTH FUNCTIONS OF GROUP ACTIONS ON A-TREES, pg. 265*RESIDUAL FINITENESS FOR 3-MANIFOLDS, pg. 379*THE NIELSEN-THURSTON THEORY OF SURFACE AUTOMORPHISMS, pg. 397*WHITEHEAD GROUPS OF CERTAIN HYPERBOLIC MANIFOLDS, II, pg. 415*CHARACTERIZATION OF FINITE SUBGROUPS OF THE MAPPING-CLASS GROUP, pg. 433*A SEQUENCE OF PSEUDO-ANOSOV DIFFEOMORPHISMS, pg. 443*DEHN'S ALGORITHM REVISITED, WITH APPLICATIONS TO SIMPLE CURVES ON SURFACES, pg. 451*PATHS OF GEODESICS AND GEOMETRIC INTERSECTION NUMBERS: I, pg. 479*PATHS OF GEODESICS AND GEOMETRIC INTERSECTION NUMBERS: II, pg. 501*SELECTED PROBLEMS, pg. 545*Backmatter, pg. 552
£113.60
Princeton University Press Metric Methods of Finsler Spaces and in the
Book SynopsisThe description for this book, Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8), will be forthcoming.Table of Contents*Frontmatter, pg. i*Preface, pg. iii*Table of Contents, pg. v*Chapter I. Metric Spaces with Geodesics, pg. 1*Chapter II. Metric Conditions for Finsler Spaces, pg. 30*Chapter III. Properties of General S. L. Spaces, pg. 72*Chapter IV. Spaces with Convex Spheres, pg. 119*Chapter V. Motions, pg. 175*Bibliography, pg. 235*Index, pg. 240
£69.70
Princeton University Press Harmonic Maps and Minimal Immersions with
Book SynopsisPresents a study of harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. This book covers the material which displays an interplay involving geometry, analysis and topology. It includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.Table of ContentsIntroductionPt. IBasic Variational and Geometrical PropertiesCh. IHarmonic maps and minimal immersionsBasic properties of harmonic maps13Minimal immersions20Ch. IIImmersions of parallel mean curvatureParallel mean curvature24Alexandrov's theorem29Ch. IIISurfaces of parallel mean curvatureTheorems of Chern and Ruh-Vilms34Theorems of Almgren-Calabi and Hopf37On the Sinh-Gordon equation40Wente's theorem42Ch. IVReduction techniquesRiemannian submersions48Harmonic morphisms and maps into a circle51Isoparametric maps54Reduction techniques58Pt. IIG-Invariant Minimal and Constant Mean Curvature ImmersionsCh. VFirst examples of reductionsG-equivariant harmonic maps64Rotation hypersurfaces in spheres74Constant mean curvature rotation hypersurfaces in R[superscript n]81Ch. VIMinimal embeddings of hyperspheres in S[superscript 4]Derivation of the equation and main theorem92Existence of solutions starting at the boundary95Analysis of the O.D.E. and proof of the main theorem102Ch. VIIConstant mean curvature immersions of hyperspheres into R[superscript n]Statement of the main theorem111Analytical lemmas114Proof of the main theorem120Pt. IIIHarmonic Maps Between SpheresCh. VIIIPolynomial mapsEigenmaps S[superscript m] [actual symbol not reproducible] S[superscript n]129Orthogonal multiplications and related constructions137Polynomial maps between spheres143Ch. IXExistence of harmonic joinsThe reduction equation151Properties of the reduced energy functional J154Analysis of the O.D.E.157The damping conditions161Examples of harmonic maps167Ch. XThe harmonic Hopf constructionThe existence theorem171Examples of harmonic Hopf constructions179[pi][subscript 3](S[superscript 2] and harmonic morphisms182Appendix 1 Second variations188Appendix 2 Riemannian immersions S[superscript m] [actual symbol not reproducible] S[superscript n]200Appendix 3 Minimal graphs and pendent drops204Appendix 4 Further aspects of pendulum type equations208References213Index224
£73.60
Princeton University Press Computers Rigidity and Moduli
Book SynopsisPresents an area of mathematical research that combines topology, geometry, and logic. This book seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity.Trade Review"This is a terrific book. It does no less than introduce an entire new field of mathematics - a truly astounding development. It will be widely read, I think, as much because of the masterful exposition as for the beautiful mathematics. Weinberger gives very clear and accessible descriptions of all the relevant tools from computability, topology, and geometry, in a friendly and engaging style. He has done the mathematical community a great service indeed." - Robin Forman, Rice University; "This book represents a very exciting new area of research at the interface of topology and logic. Written in a quite readable style, and presenting the more accessible cases in detail while giving references for the more involved results, it is a book whose methods and ideas will surely have many more significant applications over the next several years." - Kevin M. Whtye, University of Illinois at Chicago"
£62.40
Princeton University Press The Geometry and Topology of Coxeter Groups.
Book SynopsisPresents a comprehensive treatment of Coxeter groups from the viewpoint of geometric group theory. This book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincare Conjecture; and Gromov's theory of CAT(0) spaces and groups.Trade Review"This book is one of those that grows with the reader: A graduate student can learn many properties, details and examples of Coxeter groups, while an expert can read about aspects of recent results in the theory of Coxeter groups and use the book as a guide to the literature. I strongly recommend this book to anybody who has any interest in geometric group theory. Anybody who reads (parts of) this book with an open mind will get a lot out of it."--Ralf Gramlich, Mathematical Reviews "The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory."--L'Enseignement Mathematique "[An] excellent introduction to other, important aspects of the study of geometric and topological approaches to group theory. Davis's exposition gives a delightful treatment of infinite Coxeter groups that illustrates their continued utility to the field."--John Meier, Bulletin of the AMSTable of ContentsPreface xiii Chapter 1: INTRODUCTION AND PREVIEW 1 1.1 Introduction 1 1.2 A Preview of the Right-Angled Case 9 Chapter 2: SOME BASIC NOTIONS IN GEOMETRIC GROUP THEORY 15 2.1 Cayley Graphs and Word Metrics 15 2.2 Cayley 2-Complexes 18 2.3 Background on Aspherical Spaces 21 Chapter 3: COXETER GROUPS 26 3.1 Dihedral Groups 26 3.2 Reflection Systems 30 3.3 Coxeter Systems 37 3.4 The Word Problem 40 3.5 Coxeter Diagrams 42 Chapter 4: MORE COMBINATORIAL THEORY OF COXETER GROUPS 44 4.1 Special Subgroups in Coxeter Groups 44 4.2 Reflections 46 4.3 The Shortest Element in a Special Coset 47 4.4 Another Characterization of Coxeter Groups 48 4.5 Convex Subsets of W 49 4.6 The Element of Longest Length 51 4.7 The Letters with Which a Reduced Expression Can End 53 4.8 A Lemma of Tits 55 4.9 Subgroups Generated by Reflections 57 4.10 Normalizers of Special Subgroups 59 Chapter 5: THE BASIC CONSTRUCTION 63 5.1 The Space U 63 5.2 The Case of a Pre-Coxeter System 66 5.3 Sectors in U 68 Chapter 6: GEOMETRIC REFLECTION GROUPS 72 6.1 Linear Reflections 73 6.2 Spaces of Constant Curvature 73 6.3 Polytopes with Nonobtuse Dihedral Angles 78 6.4 The Developing Map 81 6.5 Polygon Groups 85 6.6 Finite Linear Groups Generated by Reflections 87 6.7 Examples of Finite Reflection Groups 92 6.8 Geometric Simplices: The Gram Matrix and the Cosine Matrix 96 6.9 Simplicial Coxeter Groups: Lann'er's Theorem 102 6.10 Three-dimensional Hyperbolic Reflection Groups: Andreev's Theorem 103 6.11 Higher-dimensional Hyperbolic Reflection Groups: Vinberg's Theorem 110 6.12 The Canonical Representation 115 Chapter 7: THE COMPLEX 123 7.1 The Nerve of a Coxeter System 123 7.2 Geometric Realizations 126 7.3 A Cell Structure on 128 7.4 Examples 132 7.5 Fixed Posets and Fixed Subspaces 133 Chapter 8: THE ALGEBRAIC TOPOLOGY OF U AND OF 136 8.1 The Homology of U 137 8.2 Acyclicity Conditions 140 8.3 Cohomology with Compact Supports 146 8.4 The Case Where X Is a General Space 150 8.5 Cohomology with Group Ring Coefficients 152 8.6 Background on the Ends of a Group 157 8.7 The Ends of W 159 8.8 Splittings of Coxeter Groups 160 8.9 Cohomology of Normalizers of Spherical Special Subgroups 163 Chapter 9: THE FUNDAMENTAL GROUP AND THE FUNDAMENTAL GROUP AT INFINITY 166 9.1 The Fundamental Group of U 166 9.2 What Is Simply Connected at Infinity? 170 Chapter 10: ACTIONS ON MANIFOLDS 176 10.1 Reflection Groups on Manifolds 177 10.2 The Tangent Bundle 183 10.3 Background on Contractible Manifolds 185 10.4 Background on Homology Manifolds 191 10.5 Aspherical Manifolds Not Covered by Euclidean Space 195 10.6 When Is a Manifold? 197 10.7 Reflection Groups on Homology Manifolds 197 10.8 Generalized Homology Spheres and Polytopes 201 10.9 Virtual Poincar'e Duality Groups 205 Chapter 11: THE REFLECTION GROUP TRICK 212 11.1 The First Version of the Trick 212 11.2 Examples of Fundamental Groups of Closed Aspherical Manifolds 215 11.3 Nonsmoothable Aspherical Manifolds 216 11.4 The Borel Conjecture and the PDn-Group Conjecture 217 11.5 The Second Version of the Trick 220 11.6 The Bestvina-Brady Examples 222 11.7 The Equivariant Reflection Group Trick 225 Chapter 12: IS CAT(0): THEOREMS OF GROMOV AND ZMOUSSONG 230 12.1 A Piecewise Euclidean Cell Structure on 231 12.2 The Right-Angled Case 233 12.3 The General Case 234 12.4 The Visual Boundary of 237 12.5 Background on Word Hyperbolic Groups 238 12.6 When Is CAT(-1)? 241 12.7 Free Abelian Subgroups of Coxeter Groups 245 12.8 Relative Hyperbolization 247 Chapter 13: RIGIDITY 255 13.1 Definitions, Examples, Counterexamples 255 13.2 Spherical Parabolic Subgroups and Their Fixed Subspaces 260 13.3 Coxeter Groups of Type PM 263 13.4 Strong Rigidity for Groups of Type PM 268 Chapter 14: FREE QUOTIENTS AND SURFACE SUBGROUPS 276 14.1 Largeness 276 14.2 Surface Subgroups 282 Chapter 15: ANOTHER LOOK AT (CO)HOMOLOGY 286 15.1 Cohomology with Constant Coefficients 286 15.2 Decompositions of Coefficient Systems 288 15.3 The W-Module Structure on (Co)homology 295 15.4 The Case Where W Is finite 303 Chapter 16: THE EULER CHARACTERISTIC 306 16.1 Background on Euler Characteristics 306 16.2 The Euler Characteristic Conjecture 310 16.3 The Flag Complex Conjecture 313 Chapter 17: GROWTH SERIES 315 17.1 Rationality of the Growth Series 315 17.2 Exponential versus Polynomial Growth 322 17.3 Reciprocity 324 17.4 Relationship with the h-Polynomial 325 Chapter 18: BUILDINGS 328 18.1 The Combinatorial Theory of Buildings 328 18.2 The Geometric Realization of a Building 336 18.3 Buildings Are CAT(0) 338 18.4 Euler-Poincar'e Measure 341 Chapter 19: HECKE-VON NEUMANN ALGEBRAS 344 19.1 Hecke Algebras 344 19.2 Hecke-Von Neumann Algebras 349 Chapter 20: WEIGHTED L2-(CO)HOMOLOGY 359 20.1 Weighted L2-(Co)homology 361 20.2 Weighted L2-Betti Numbers and Euler Characteristics 366 20.3 Concentration of (Co)homology in Dimension 0 368 20.4 Weighted Poincar'e Duality 370 20.5 A Weighted Version of the Singer Conjecture 374 20.6 Decomposition Theorems 376 20.7 Decoupling Cohomology 389 20.8 L2-Cohomology of Buildings 394 Appendix A: CELL COMPLEXES 401 A.1 Cells and Cell Complexes 401 A.2 Posets and Abstract Simplicial Complexes 406 A.3 Flag Complexes and Barycentric Subdivisions 409 A.4 Joins 412 A.5 Faces and Cofaces 415 A.6 Links 418 Appendix B: REGULAR POLYTOPES 421 B.1 Chambers in the Barycentric Subdivision of a Polytope 421 B.2 Classification of Regular Polytopes 424 B.3 Regular Tessellations of Spheres 426 B.4 Regular Tessellations 428 Appendix C: THE CLASSIFICATION OF SPHERICAL AND EUCLIDEAN COXETER GROUPS 433 C.1 Statements of the Classification Theorems 433 C.2 Calculating Some Determinants 434 C.3 Proofs of the Classification Theorems 436 Appendix D: THE GEOMETRIC REPRESENTATION 439 D.1 Injectivity of the Geometric Representation 439 D.2 The Tits Cone 442 D.3 Complement on Root Systems 446 Appendix E: COMPLEXES OF GROUPS 449 E.1 Background on Graphs of Groups 450 E.2 Complexes of Groups 454 E.3 The Meyer-Vietoris Spectral Sequence 459 Appendix F: HOMOLOGY AND COHOMOLOGY OF GROUPS 465 F.1 Some Basic Definitions 465 F.2 Equivalent (Co)homology with Group Ring Coefficients 467 F.3 Cohomological Dimension and Geometric Dimension 470 F.4 Finiteness Conditions 471 F.5 Poincar'e Duality Groups and Duality Groups 474 Appendix G: ALGEBRAIC TOPOLOGY AT INFINITY 477 G.1 Some Algebra 477 G.2 Homology and Cohomology at Infinity 479 G.3 Ends of a Space 482 G.4 Semistability and the Fundamental Group at Infinity 483 Appendix H: THE NOVIKOV AND BOREL CONJECTURES 487 H.1 Around the Borel Conjecture 487 H.2 Smoothing Theory 491 H.3 The Surgery Exact Sequence and the Assembly Map Conjecture 493 H.4 The Novikov Conjecture 496 Appendix I: NONPOSITIVE CURVATURE 499 I.1 Geodesic Metric Spaces 499 I.2 The CAT(?)-Inequality 499 I.3 Polyhedra of Piecewise Constant Curvature 507 I.4 Properties of CAT(0) Groups 511 I.5 Piecewise Spherical Polyhedra 513 I.6 Gromov's Lemma 516 I.7 Moussong's Lemma 520 I.8 The Visual Boundary of a CAT(0)-Space 524 Appendix J: L2-(CO)HOMOLOGY 531 J.1 Background on von Neumann Algebras 531 J.2 The Regular Representation 531 J.3 L2-(Co)homology 538 J.4 Basic L2 Algebraic Topology 541 J.5 L2-Betti Numbers and Euler Characteristics 544 J.6 Poincar'e Duality 546 J.7 The Singer Conjecture 547 J.8 Vanishing Theorems 548 Bibliography 555 Index 573
£92.00
Princeton University Press NonArchimedean Tame Topology and Stably Dominated
Book SynopsisOver the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools. For non-archimedTrade Review"A major achievement, both in rigid algebraic geometry, and as an application of model-theoretic and stability-theoretic methods to algebraic geometry."---Anand Pillay, MathSciNetTable of Contents*Frontmatter, pg. i*Contents, pg. v*1. Introduction, pg. 1*2. Preliminaries, pg. 8*3. The space v of stably dominated types, pg. 37*4. Definable compactness, pg. 57*5. A closer look at the stable completion, pg. 70*6. GAMMA-internal spaces, pg. 76*7. Curves, pg. 92*8. Strongly stably dominated points, pg. 104*9. Specializations and ACV2F, pg. 119*10. Continuity of homotopies, pg. 142*11. The main theorem, pg. 154*12. The smooth case, pg. 177*13. An equivalence of categories, pg. 183*14. Applications to the topology of Berkovich spaces, pg. 187*Bibliography, pg. 207*Index, pg. 211*List of notations, pg. 215
£130.40
Princeton University Press NonArchimedean Tame Topology and Stably Dominated
Book SynopsisTrade Review"A major achievement, both in rigid algebraic geometry, and as an application of model-theoretic and stability-theoretic methods to algebraic geometry."---Anand Pillay, MathSciNetTable of Contents*Frontmatter, pg. i*Contents, pg. v*1. Introduction, pg. 1*2. Preliminaries, pg. 8*3. The space v of stably dominated types, pg. 37*4. Definable compactness, pg. 57*5. A closer look at the stable completion, pg. 70*6. GAMMA-internal spaces, pg. 76*7. Curves, pg. 92*8. Strongly stably dominated points, pg. 104*9. Specializations and ACV2F, pg. 119*10. Continuity of homotopies, pg. 142*11. The main theorem, pg. 154*12. The smooth case, pg. 177*13. An equivalence of categories, pg. 183*14. Applications to the topology of Berkovich spaces, pg. 187*Bibliography, pg. 207*Index, pg. 211*List of notations, pg. 215
£60.00
Princeton University Press The Structure of Groups with a Quasiconvex
Book Synopsis
£124.00
Princeton University Press The Structure of Groups with a Quasiconvex
Book Synopsis
£56.00
Princeton University Press Fourier Restriction for Hypersurfaces in Three
Book SynopsisTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Chapter 1. Introduction, pg. 1*Chapter 2. Auxiliary Results, pg. 29*Chapter 3. Reduction to Restriction Estimates near the Principal Root Jet, pg. 50*Chapter 4. Restriction for Surfaces with Linear Height below 2, pg. 57*Chapter 5. Improved Estimates by Means of Airy-Type Analysis, pg. 75*Chapter 6. The Case When hlin(PHI) => 2: Preparatory Results, pg. 105*Chapter 7. How to Go beyond the Case hlin(PHI) => 5, pg. 131*Chapter 8. The Remaining Cases Where m = 2 and B = 3 or B = 4, pg. 181*Chapter 9. Proofs of Propositions 1.7 and 1.17, pg. 244*Bibliography, pg. 251*Index, pg. 257
£130.40
Princeton University Press The Seduction of Curves
Book SynopsisA lavishly illustrated book that explores the language of curves that spans the human body, science, engineering, and artCurves are seductive. These smooth, organic lines and surfaces-like those of the human body-appeal to us in an instinctive, visceral way that straight lines or the perfect shapes of classical geometry never could. In this large-fTrade Review"One of Choice Reviews' Outstanding Academic Titles of 2018""I have never encountered anything quite like [The Seduction of Curves], which I view as genuinely sui generis. . . . The (excellent) prose descriptions are accompanied by lots of illustrations, both photographs and drawings, quite a few of which are in color. . . . An unusual and eclectic book, and one that taught me a lot of things that I did not know before."---Mark Hunacek, MAA Reviews"To illustrate this little-known branch of mathematics, [Allan McRobie] draws on the art of David Hockney, Henry Moore and Salvador Dalí, as well as Helena Weightman's superb photographs of mountains, mushrooms, reflections on water and naked bodies."---Matthew Reisz, Times Higher Education"Stunning. . . . The balance is such that it should appeal both to art lovers and those with a real interest in the mathematical basis."---Brian Clegg, Popular Science"Marvelous."---Adhemar Bultheel, European Mathematical Society"Can you find your own butterflies, swallowtails and wigwams? They are right there on your body: the geometrical figures that appear when smoothly curved surfaces are viewed from the right angle. Structural engineer Allan McRobie's The Seduction of Curves is your guide to these most intimate of mathematical objects."---Philip Ball, New Scientist"A delightful journey beyond disciplines. . . . The book intends to lead readers to see the world differently and I believe that in many cases it will, linking subtle mathematical ideas to the world they are surrounded by."---Edmund O. Harriss, MathSciNet"This book is a bold attempt at evoking multiple feelings towards curves. Allan McRobie deserves praise for sensually drawing parallels between the natural and constructed worlds."---Sudhirendar Sharma, Current Science"Both immediate and analytical, beautiful and informative, The Seduction of Curves is a successful hybrid of art book, representation of descriptive geometry, and explanation of mathematical concepts . . . . a book that entertains and teaches, pleases and challenges in equal measure."---Hans J. Rindisbach, European Legacy"Remarkable. . . . Successful . . . due to the erudition of the author plus the quality of the production both in the illustrations used and in the general elegance of the book itself. It would grace the grandest of coffee tables and provide the basis for interesting debates."---Phil Dyke, Leonardo ReviewsTable of Contents1 The Alphabet of Beautiful Curves 12 The Fold 53 The Cusp 144 The Swallowtail 225 The Butterfly 316 The Wigwam 357 Lips, Beaks, Gull, Goose 378 The Persistence of Cusps 439 Moire and Dupin 4710 The Umbilics 6111 Catastrophe Optics 6712 The Rainbow 7313 Gravitational Lenses 7714 Stability 8515 Morphogenesis 8816 Gabo 9417 The Pregnance of Curves 11718 Thom 12519 Dali 135Notes 147Bibliography 151Image Credits 153Index 157
£27.00
Princeton University Press The Norm Residue Theorem in Motivic Cohomology
Book Synopsis
£130.40
Princeton University Press The Norm Residue Theorem in Motivic Cohomology
Book Synopsis
£60.00
Princeton University Press Introductory Lectures on Equivariant Cohomology
Book SynopsisTrade Review"Very well-written, self contained and gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology."---Marek Golasiński, Zentralblatt MATH
£130.40
Princeton University Press Introductory Lectures on Equivariant Cohomology
Book Synopsis
£60.00
Princeton University Press Visual Differential Geometry and Forms A
Book SynopsisTrade Review"Finalist for the PROSE Award in Mathematics, Association of American Publishers""Needham proposes to provide a truly geometric 'visual' explication of differential geometry, and he succeeds brilliantly. I know nothing like it in the literature."---Frank Morgan, EMS Magazine"[The] book offers a truly unique and original take on differential geometry, and it amply deserves inclusion within the pantheon of textbook deities."---Eric Poisson, Notices of the AMS"This is a valuable and beautifully created guide to what can at first seem a confusing area of mathematical physics. There are other contenders that try to teach this subject, but this is the best that I have come across so far and I will continue to enjoy learning from it (and almost certainly teaching from it) over the coming years, I am sure."---Jonathan Shock, Mathemafrica"[Proactively] rethinks the way this important area of mathematics should be considered and taught." * MathSciNet *"The book is a remarkable and highly original approach to the basic stem of differential geometry. And that mathematical trunk has roots and branches in so many other unexpected yet related subjects, each of which can be equally well approached from the same geometrical point of view."---Adhemar Bultheel, MAA Reviews"[Visual Differential Geometry and Forms] its peers. It is fun to read and provides a unique and intuitive approach to differential geometry. The author’s passion for the subject is evident throughout the book. Although Needham’s approach is unorthodox, it is rewarding, and complements the exposition found in standard textbooks."---Sean M. Eli & Krešmir Josić, SIAM Review
£100.30
Princeton University Press Foundations of Algebraic Topology
Book SynopsisTable of Contents*Frontmatter, pg. i*Preface, pg. vii*Contents, pg. xv*I. Axioms and general theorems, pg. 1*II. Simplicial complexes, pg. 54*III. Homology theory of simplicial complexes, pg. 76*IV. Categories and functors, pg. 108*V. Chain complexes, pg. 124*VI. Formal homology theory of simplicial complexes, pg. 162*VII. The singular homology theory, pg. 185*VIII. Systems of groups and their limits, pg. 212*IX. The Cech homology theory, pg. 233*X. Special features of the Cech theory, pg. 257*XI. Applications to Euclidean Spaces, pg. 298*Index, pg. 323
£49.30
Institute of Physics Publishing Differential Topology and Geometry with
Book SynopsisThis book presents, in a concise and direct manner, the appropriate mathematical formalism and fundamentals of differential topology and differential geometry, together with essential applications in many branches of physics.
£89.10
Springer Exercises in Basic Ring Theory 20 Texts in the
Book SynopsisOur intention was to provide a collection of exercises which cover only the easy part of ring theory, what we have named the "Basics of Ring Theory". The book is divided in two parts each consisting of seventeen chapters, the first part containing the exercises and the second part the solutions.Table of ContentsPreface. List of Symbols. I: Exercises. 1. Fundamentals. 2. Ideals. 3. Zero Divisors. 4. Ring Homomorphisms. 5. Characteristics. 6. Divisibility in Integral Domains. 7. Division Rings. 8. Automorphisms. 9. The Tensor Product. 10. Artinian and Noetherian Rings. 11. Socle and Radical. 12. Semisimple Rings. 13. Prime Ideals, Local Rings. 14. Polynomial Rings. 15. Rings of Quotients. 16. Rings of Continuous Functions. 17. Special Problems. II: Solutions. 1. Fundamentals. 2. Ideals. 3. Zero Divisors. 4. Ring Homomorphisms. 5. Characteristics. 6. Divisibility in Integral Domains. 7. Division Rings. 8. Automorphisms. 9. The Tensor Product. 10. Artinian and Noetherian Rings. 11. Socle and Radical. 12. Semisimple Rings. 13. Prime Ideals, Local Rings. 14. Polynomial Rings. 15. Rings of Quotients. 16. Rings of Continuous Functions. 17. Special Problems. Bibliography. Index.
£42.74
Birkhauser Boston Metric Structures for Riemannian and
Book SynopsisPreface to the French Edition.- Preface to the English Edition.- Introduction: Metrics Everywhere.- Length Structures: Path Metric Spaces.- Degree and Dilatation.- Metric Structures on Families of Metric Spaces.- Convergence and Concentration of Metrics and Measures.- Loewner Rediscovered.- Manifolds with Bounded Ricci Curvature.- Isoperimetric Inequalities and Amenability.- Morse Theory and Minimal Models.- Pinching and Collapse.- Appendix A: 'Quasiconvex' Domains in Rn.- Appendix B: Metric Spaces and Mappings Seen at Many Scales.- Appendix C: Paul Levy's Isoperimetric Inequality.- Appendix D: Systolically Free Manifolds.- Bibliography.- Glossary of Notation.- Index.Trade ReviewFrom the reviews:"The book gives genius insight into the connections between topology and Riemannian geometry, geometry and probability, geometry and analysis, respectively. The huge variety of progressive key ideas could provide numerous research problems in the next decades." —Publicationes Mathematicae "This book will become one of the standard references in the research literature on the subject. Many fascinating open problems are pointed out. Since this domain has dramatically exploded since 1979 and also is one which has many contact points with diverse areas of mathematics, it is no small task to present a treatment which is at once broad and coherent. It is a major accomplishment of Misha Gromov to have written this exposition. It is hard work to go through the book, but it is worth the effort." —Zentralblatt Math"The first edition of this book...is considered one of the most influential books in geometry in the last twenty years... Among the most substantial additions [of the 2/e]...is a chapter on convergence of metric spaces with measures, and an appendix on analysis on metric spaces... In addition, numerous remarks, examples, proofs, and open problems are inserted throughout the book. The original text is preserved with new items conveniently indicated... This book is certain to be a source of inspiration for many researchers as well as required reading for students entering the subject." —Mathematical Reviews“This is a reprint of the 2001 edition of Gromov’s by now classical book on metric structures. … this work will continue to set the standard in the field for the foreseeable future.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 156 (4), April, 2009)Table of ContentsLength Structures: Path Metric Spaces.- Degree and Dilatation.- Metric Structures on Families of Metric Spaces.- Convergence and Concentration of Metrics and Measures.- Loewner Rediscovered.- Manifolds with Bounded Ricci Curvature.- Isoperimetric Inequalities and Amenability.- Morse Theory and Minimal Models.- Pinching and Collapse.
£98.99
Birkhauser Boston Inc Knot Theory and Its Applications Modern Birkhuser
Book SynopsisFundamental Concepts of Knot Theory.- Knot Tables.- Fundamental Problems of Knot Theory.- Classical Knot Invariants.- Seifert Matrices.- Invariants from the Seifert Matrix.- Torus Knots.- Creating Manifolds from Knots.- Tangles and 2-Bridge Knots.- The Theory of Braids.- The Jones Revolution.- Knots via Statistical Mechanics.- Knot Theory in Molecular Biology.- Graph Theory Applied to Chemistry.- Vassiliev Invariants.Trade ReviewFrom the reviews: "The book ...develops knot theory from an intuitive geometric-combinatorial point of view, avoiding completely more advanced concepts and techniques from algebraic topology.... intended for readers without a considerable background in mathematics...particular attention is given to connections and applications to other natural sciences. Thus the emphasis is on a lucid and intuitive exposition accessible to a broader audience... The book, written in a stimulating and original style, will serve as a first approach to this interesting field for readers with various backgrounds in mathematics, physics, etc. It is the first text developing recent topics as the Jones polynomial and Vassiliev invariants on a level accessible also for non-specialists in the field." –Zentralblatt Math "Noteworthy features here include applications to chemistry and biology and a final chapter on the very important Vassiliev invariants, a fairly late-breaking development. Murasugi, an expert of stature on knots, begins absolutely from first principles and avoids sophisticated terminology, but he writes in a careful and rigorous style." –Choice "I grabbed the opportunity to review this book, and I’m still enthusiastic. … I enjoyed it immensely. … In general, the author strives for clarity, and that was appreciated by this reviewer and will be appreciated by students. … I also enjoyed how he always keeps us abreast of the general picture, in particular keeping us up to date with respect to the various new results and successes … ." (Marion Cohen, MathDL, June, 2008)Table of ContentsFundamental Concepts of Knot Theory.- Knot Tables.- Fundamental Problems of Knot Theory.- Classical Knot Invariants.- Seifert Matrices.- Invariants from the Seifert Matrix.- Torus Knots.- Creating Manifolds from Knots.- Tangles and 2-Bridge Knots.- The Theory of Braids.- The Jones Revolution.- Knots via Statistical Mechanics.- Knot Theory in Molecular Biology.- Graph Theory Applied to Chemistry.- Vassiliev Invariants.
£52.24
