Topology Books
The University of Chicago Press Geometry of Nonpositively Curved Manifolds
Book SynopsisStarting from the foundations, this text presents an almost entirely self-contained treatment of differentiable spaces of nonpositive curvature, focusing on the symmetric spaces in which every geodesic lies in a flat Euclidean space of dimension at least two.
£117.80
The University of Chicago Press Geometry Rigidity and Group Actions
Book SynopsisExplores the role of group actions and rigidity in several areas of mathematics, including ergodic theory, dynamics, geometry, topology, and the algebraic properties of representation varieties.
£72.20
The University of Chicago Press Topics in Geometric Group Theory
Book SynopsisThis work seeks to offer a concise introduction to geometric group theory - a method for studying infinite groups via their intrinsic geometry. Basic combinatorial and geometric group theory is presented, along with research on the growth of groups, and exercises and problems.
£34.20
The University of Chicago Press Lie Algebras and Locally Compact Groups Chicago
Book SynopsisThis volume presents lecture notes based on the author's courses on Lie algebras and the solution of Hilbert's fifth problem. In chapter 1, Lie Algebras, the structure theory of semi-simple Lie algebras in characteristic zero is presented, following the ideas of Killing and Cartan. Chapter 2, The Structure of Locally Compact Groups, deals with the solution of Hilbert's fifth problem given by Gleason, Montgomery, and Zipplin in 1952.
£38.00
The University of Chicago Press Groups of Circle Diffeomorphisms
Book SynopsisGroup actions are an efficient way of describing symmetries in objects by defining the essential elements of a given object as a set. The symmetries of the object are then defined as the symmetry group of this set. This title explores group actions on the simplest closed manifold, the circle.
£42.75
The University of Chicago Press The Topological Classification of Stratified
Book SynopsisThis text provides topologists with a new way of looking at the classification theory of singular spaces. Divided into three parts, the book begins with an overview of high-dimensional manifold theory. It then offers the parallel theory for stratified spaces. Applications are also included.Table of ContentsPart 1 Manifold theory: algebraic K-theory and topology; surgery theory; spacification and functoriality; applications. Part 2 General theory: definitions and examples; classification of stratified spaces; transverse stratified classification; PT category; controlled topology; proof of main theorems in topology. Part 3 Applications and illustrations: manifolds and embedding theory revisited; supernormal spaces and varieties; group actions; rigidity conjectures.
£30.00
The University of Chicago Press Geometrical Vectors
Book SynopsisA guide for any student of vector analysis, this text separates those relationships which are topologically invariant from those which are not. Based on the essentially geometric nature of the subject, this approach builds consistently on students' prior knowledge and geometrical intuition.
£28.00
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
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
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
£74.80
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
£120.70
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"
£70.20
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
£138.55
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
£63.75
Princeton University Press The Structure of Groups with a Quasiconvex
Book Synopsis
£131.75
Princeton University Press The Structure of Groups with a Quasiconvex
Book Synopsis
£63.00
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
£138.55
Princeton University Press Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra
a huge range and FREE tracked UK delivery on ALL orders.
£63.75
Princeton University Press The Norm Residue Theorem in Motivic Cohomology
Book Synopsis
£138.55
Princeton University Press The Norm Residue Theorem in Motivic Cohomology
Book Synopsis
£63.75
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
£138.55
Princeton University Press Introductory Lectures on Equivariant Cohomology
Book Synopsis
£63.75
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
£106.20
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
American Mathematical Society Fundamentals of the Theory of Operator Algebras
Book SynopsisPresents an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide an account of the introductory portions of this important and technically difficult subject.Table of ContentsLinear spaces Basics of Hilbert space and linear operators Banach algebras Elementary $C^*$-algebra theory Elementary von Neumann algebra theory Bibliography Index of notation Index.
£79.20
MP-AMM American Mathematical Groups and Geometric Analysis Integral Geometry
Book SynopsisGroup-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group.Trade ReviewFrom reviews of the original edition:""The book is excellent both as a text and as a reference work; it will clearly become another instant classic."" —American Scientist""This volume makes an excellent companion to the author's Differential Geometry, Lie Groups, and Symmetric Spaces, putting to work many of the abstract concepts developed in the earlier volume. The introductory material and large number of exercises (with answers!) will make the book quite appropriate for students. Researchers will find numerous useful references on geometric analysis, along with proofs, connections with other parts of mathematics, and valuable historical remarks. This book, like the author's previous work on differential geometry, will no doubt inspire considerable further research and become the standard text on the subjects it covers."" —Mathematical Reviews""Few treatises today can lay claim to being ""aere perennius"", but all of Helgason's books certainly do with a vengeance ... [He] sets a model of style and clarity that has not been matched since Enriques's Geometria proiettiva. This is the kind of mathematics that will live forever."" —The Bulletin of Mathematics Books""A most valuable contribution to Lie theory and to the interplay between geometry and analysis. It is remarkable that the beautiful theory in Chapter IV can be presented in a textbook form with complete proofs."" —Bulletin of the London Mathematical Society""The diversity of subjects treated is great. Nevertheless the author has managed to achieve coherence of presentation by clearly putting forward a few main themes and basic problems. The first third of the book is suitable as a text for beginning graduate students; the book is also an excellent source of reference for experts. No doubt it will become a new standard in the field."" —CWI QuarterlyTable of Contents Geometric Fourier analysis on spaces of constant curvature Integral geometry and Radon transforms Invariant differential operators Invariants and harmonic polynomials Spherical functions and spherical transforms Analysis on compact symmetric spaces Appendix Some details Bibliography Symbols frequently used Index Errata
£101.70
MP-AMM American Mathematical Fixed Points
Book SynopsisPresents an exposition of fixed point theory. This work focuses on the problem of whether a closed interval, square, disk, or sphere has the fixed point property. It aims to show how fixed point theory uses combinatorial ideas related to decomposition of figures into distinct parts called faces, which adjoin each other in a regular fashion.Table of ContentsContinuous mappings of a closed interval and a square First combinatorial lemma Second combinatorial lemma, or walks through the rooms in a house Sperner's lemma Continuous mappings, homeomorphisms, and the fixed point property Compactness Proof of Brouwer's Theorem for a closed interval, the intermediate value theorem, and applications Proof of Brouwer's Theorem for a square The iteration method Retraction Continuous mappings of a circle, homotopy, and degree of a mapping Second definition of the degree of a mapping Continuous mappings of a sphere Lemma on equality of degrees.
£35.96
Springer-Verlag New York Inc. An Invitation to Morse Theory
Book SynopsisThis self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also be of interest to researchers.This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory.The reader is expected to have some familiarity with cohomology theory and differential and integral calculus on smooth manifolds.Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition.Trade ReviewFrom the reviews:"Morse theory, a tool within differential topology, strategically studies a given abstract smooth manifold by first imposing on it a nearly arbitrary numerical function, and then cleverly extracting from it purely topological information. … Undergraduates will see that the foundations of this advanced topic build directly on a(n honest) course in multivariable calculus … . Primarily for mathematics students. Summing Up: Recommended. Upper-division undergraduates through professionals." (D. V. Feldman, CHOICE, Vol. 45 (6), February, 2008)"The book is a nicely written self-contained introduction to Morse theory … will be useful for mathematicians of various levels, including graduate students and researchers." (Michael Farber, Zentralblatt MATH, Vol. 1131, 2008)"Nicolaescu’s book starts with the basics of Morse theory over the reals … . The discussion continuously presents some really nice and well chosen applications of the theory, and finally lets the reader see, that the whole theory can go on to complex, where the set of regular values, that is disconnected by nature over the reals, becomes connected. … This book is warmly recommended for interested graduate students and researcher … ." (Árpád Kurusa, Acta Scientiarum Mathematicarum, Vol. 74, 2008)"Nicolaescu’s book complements previous books on Morse theory by quickly developing the foundations of the subject in terms of gradient-like vector fields and discussing applications not found in other books on Morse theory. … the book is recommended for graduate students and researchers … ." (David E. Hurtubise, Mathematical Reviews, Issue 2009 m)From the reviews of the second edition:“The present book provides a wonderful presentation of concepts and ideas as well as problems with their solutions in Morse Theory, an important and challenging part of Differential Topology. … The book ends with an useful and relevant bibliography containing 85 references. It also contains an index of symbols and a subject index. … ‘The book will be useful for mathematicians of various levels, including graduate students and researchers’.” (Dorin Andrica, Zentralblatt MATH, Vol. 1238, 2012)Table of ContentsPreface.- Notations and Conventions.- 1 Morse Functions.- 2 The Topology of Morse Functions.- 3 Applications.- 4 Morse-Smale Flows and Whitney Stratifications.- 5 Basics of Complex Morse Theory.- 6 Exercises and Solutions.- References.- Index
£999.99
Springer-Verlag New York Inc. Graphs on Surfaces Dualities Polynomials and
Book Synopsis Graphs on Surfaces: Dualities, Polynomials, and Knots also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knot theorists.Trade ReviewFrom the reviews:“Here, the venerable knot-theoretic and graph-theoretic themes find a host of unifying common generalizations. Undergraduates will appreciate the patient and visual development of the foundations, particularly the dualities (paired representations of a single structure). Summing Up: Recommended. Upper-division undergraduates through researchers/faculty.” (D. V. Feldman, Choice, Vol. 51 (7), March, 2014)“This monograph is aimed at researchers both in graph theory and in knot theory. It should be accessible to a graduate student with a grounding in both subjects. There are (colour) diagrams throughout. … The monograph gives a unified treatment of various ideas that have been studied and used previously, generalising many of them in the process.” (Jessica Banks, zbMATH, Vol. 1283, 2014)“The authors have composed a very interesting and valuable work. … For properly prepared readers … the book under review is the occasion for all sorts of fun including the inner life of ribbon groups, Tait graphs, Penrose polynomials, Tutte polynomials, and of course Jones polynomials and HOMFLY polynomials. This is fascinating mathematics, presented in a clear and accessible way.” (Michael Berg, MAA Reviews, October, 2013)Table of Contents1. Embedded Graphs .- 2. Generalised Dualities .- 3. Twisted duality, cycle family graphs, and embedded graph equivalence .- 4. Interactions with Graph Polynomials .- 5. Applications to Knot Theory .- References .- Index .
£56.99
MP-AMM American Mathematical Winding Around
Book SynopsisTrade ReviewThis book covers a lot of ground. But it does so in a clear and careful manner that would make a terrific read for the prepared undergraduate. It is a study in how an intuitive idea can transport one into some deep waters of mathematics, and that is an important story to tell." - John McCleary, Mathematical Reviews"People who teach university-level mathematics for a living often find themselves reading lots of books on the subject. But even for the book-lovers among us, after you've just read about ten linear algebra texts, all of which look like they were stamped from the same cookie cutter, the process can occasionally wear thin. It's very pleasant, then, to stumble across a book that is genuinely unique, that addresses a topic in a way not found elsewhere, and that teaches you something that you didn't know before. It's even nicer when the book in question does a really good job of it, as is the case with the book under review. ...Roe's writing style is succinct, but clear and quite elegant; I could practically hear a British accent as I read the book. This clarity of writing and the numerous appendices help make the book accessible." - MAA OnlineTable of Contents Prelude: Love, hate, and exponentials Paths and homotopies The winding number Topology of the plane Integrals and the winding number Vector fields and the rotation number The winding number in functional analysis Coverings and the fundamental group Coda: The Bott periodicity theorem Linear algebra Metric spaces Extension and approximation theorems Measure zero Calculus on normed spaces Hilbert space Groups and graphs Bibliography Index
£47.70
MP-AMM American Mathematical Differential Geometry Curves Surfaces
Book SynopsisOffers an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples.Trade ReviewThe book provides an excellent introduction to the differential geometry of curves, surfaces and Riemannian manifolds that should be accessible to a variety of readers… Frankly, this is a great book… even after only two chapters the reader is exposed to a lot of interesting mathematics. If you are looking to teach or learn differential geometry at an introductory level, Differential Geometry Curves—Surfaces—Manifolds is a great resource to have on hand." - Jason M. Graham, MAA ReviewsTable of Contents Notations and prerequisites from analysis Curves in $\mathbb{R}^n$ The local theory of surfaces The intrinsic geometry of surfaces Riemannian manifolds The curvature tensor Spaces of constant curvature Einstein spaces Solutions to selected exercises Bibliography List of notation Index
£46.80
MP-AMM American Mathematical From Frenet to Cartan The Method of Moving Frames
Book SynopsisOffers an introduction to the method of moving frames as developed by Cartan, at a level suitable for beginning graduate students familiar with the geometry of curves and surfaces in Euclidean space. The main focus is on the use of this method to compute local geometric invariants for curves and surfaces in various 3-dimensional homogeneous spaces.Trade ReviewAn excellent and unique graduate level exposition of the differential geometry of curves, surfaces and higher-dimensional submanifolds of homogeneous spaces based on the powerful and elegant method of moving frames. The treatment is self-contained and illustrated through a large number of examples and exercises, augmented by Maple code to assist in both concrete calculations and plotting. Highly recommended." — Niky Kamran, McGill University"The method of moving frames has seen a tremendous explosion of research activity in recent years, expanding into many new areas of applications, from computer vision to the calculus of variations to geometric partial differential equations to geometric numerical integration schemes to classical invariant theory to integrable systems to infinite-dimensional Lie pseudo-groups and beyond. Cartan theory remains a touchstone in modern differential geometry, and Clelland's book provides a fine new introduction that includes both classic and contemporary geometric developments and is supplemented by Maple symbolic software routines that enable the reader to both tackle the exercises and delve further into this fascinating and important field of contemporary mathematics. Recommended for students and researchers wishing to expand their geometric horizons." — Peter Olver, University of MinnesotaTable of Contents Background material: Assorted notions from differential geometry Differential forms Curves and surfaces in homogeneous spaces via the method of moving frames: Homogeneous spaces Curves and surfaces in Euclidean space Curves and surfaces in Minkowski space Curves and surfaces in equi-affine space Curves and surfaces in projective space Applications of moving frames: Minimal surfaces in $\mathbb{E}^3$ and $\mathbb{A}^3$ Pseudospherical surfaces in Backlund's theorem Two classical theorems Beyond the flat case: Moving frames on Riemannian manifolds: Curves and surfaces in elliptic and hyperbolic spaces The nonhomogeneous case: Moving frames on Riemannian manifolds Bibliography Index.
£999.99
MP-AMM American Mathematical Probabilistic Methods in Geometry Topology and
Book SynopsisContains the proceedings of the CRM Workshops on Probabilistic Methods in Spectral Geometry and PDE, held in 2016 at the Centre de Recherches Mathematiques. This volume covers developments in active research areas at the interface of Probability, Semiclassical Analysis, Mathematical Physics, Theory of Automorphic Forms and Graph Theory.Table of Contents L. Chen and N. Shu, A geometric treatment of log-correlated Gaussian free fields S. Eswarathasan, Tangent nodal sets for random spherical harmonics J. Friedman, Formal zeta function expansions and the frequency of Ramanujan graphs D. Jakobson, T. Langsetmo, I. Rivin, and L. Turner, Rank and Bollobas-Riordan polynomials: Coefficient measures and zeros V. Konakov, S. Menozzi, and S. Molchanov, The Brownian motion on $\mathrm{Aff}(\mathbb{R})$ and quasi-local theorems N. Laaksonen, Quantum limits of Eisenstein series in $\mathbb{H}^3$ F. Macia and G. Riviere, Observability amd quantum limits for the Schrodinger equation on $\mathbb{S}^d$ M. Rossi, Random nodal lengths and Wiener chaos L. Silberman and A. Venkatesh, Entropy bounds and quantum unique ergodity for Hecke eigenfunctions on division algebras.
£103.50
MP-AMM American Mathematical Introduction to the Theory of Valuations
Book SynopsisTable of Contents Basic definitions and examples McMullen's decomposition theorem Valuations on the line McMullen's description of $(n-1)$-homogeneous valuations The Klain-Schneider characterization of simple valuations Digression on the theory of generalized functions on manifolds The Goodey-Weil imbedding Digression on vector bundles The irreducibility theorem Further developments Bibliography
£44.06
MP-AMM American Mathematical GromovWitten Theory of Quotients of Fermat
Book Synopsis
£68.40
MP-AMM American Mathematical Topology and Geometry of Biopolymers
Book SynopsisContains the proceedings of the AMS Special Session on Topology of Biopolymers, held April 2018, at Northeastern University. The papers cover recent results on the topology and geometry of DNA and protein knotting using techniques from knot theory, spatial graph theory, differential geometry, molecular simulations, and laboratory experimentation.Table of Contents The topology and geometry of DNA: J. M. Fogg and L. Zechiedrich, Beyond the static DNA model of Watson and Crick P. Liu, R. Polischuk, Y. Diao, and J. Arsuaga, Characterizing the topology of kinetoplast DNA using random knotting A. Kasman and B. LeMesurier, Did sequence dependent geometry influence the evolution of the genetic code? T. Deguchi and E. Uehara, Topological sum rules in the knotting probabilities of DNA D. Buck and D. O'Donnol, Knotting of replication intermediates is narrowly restricted A. H. Moore and M. Vazquez, Recent advances on the non-coherent band surgery model for site-specific recombination The topology and geometry of proteins: S. E. Jackson, Why are there knots in proteins? A. Nunes and P. F. N. Faisca, Knotted proteins: Tie etiquette in structural biology D. Goundaroulis, J. Dorier, and A. Stasiak, Knotoids and protein structure K. C. Millett, Topological linking and entanglement in proteins E. Panagiotou and K. W. Plaxco, A topological study of protein folding kinetics.
£96.30
MP-AMM American Mathematical Ktheory in Algebra Analysis and Topology
Book SynopsisContains the proceedings of the ICM 2018 satellite school and workshop $K$-theory conference in Argentina. The volume showcases current developments in $K$-theory and related areas, including motives, homological algebra, index theory, operator algebras, and their applications and connections.Table of Contents P. Bressler, A. Gorokhovsky, R. Nest, and B. Tsygan, Comparison of spaces associated to DGLA via higher holonomy U. Bunke, A. Engel, D. Kasprowski, and C. Winges, Equivariant coarse homotopy theory and coarse algebraic K-homology A. Buss, S. Echterhoff, and R. Willett, Injectivity, crossed products, and amenable group actions L. Hesselholt and T. Nikolaus, Algebraic $K$-theory of planar cuspidal curves D. Juan-Pineda, On $NK_0$ of the group of quaternions M. Karoubi and C. Weibel, The Witt group of real surfaces A. Krishna and H. P. Sarwar, Negative $K$-theory and Chow group of monoid algebras S. T. Melo, The principal-symbol index map for an algebra of pseudodifferential operators R. Meyer, A more general method to classify up to equivariant KK-equivalence II: Computing obstruction classes A. Neeman, Grothendieck duality made simple J. Park, Calculus of absolute Kahler forms and Milnor $K$-theory G. Tabuada, Noncommutative counterparts of celebrated conjectures R. Willett, Bott periodicity and almost commuting matrices.
£94.50
MP-AMM American Mathematical Noncommutative Geometry Quantum Fields and
Book SynopsisThe unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role.Trade Review...the authors manage very well in filtering and presenting the central ideas whilst including a rich and precise list of references to the literature. ...will undoubtedly serve as an inspiration to the formidable mathematical question on the structure of the following two spaces: spacetime and the space of primes."" - Mathematical ReviewsTable of Contents Quantum fields, noncommutative spaces, and motives The Riemann zeta function and noncommutative geometry Quantum statistical mechanics and Galois symmetries Endomotives, thermodynamics, and the Weil explicit formula Appendix Bibliography Index.
£78.30
MP-AMM American Mathematical Sutured ECH is a Natural Invariant
Book Synopsis
£67.50
MP-AMM American Mathematical Dynamics Topology and Numbers
Book SynopsisContains the proceedings of the conference Dynamics: Topology and Numbers, held in July 2018. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics.Table of Contents L. Snoha, The life and mathematics of Sergii Kolyada I. Kolyada, A. Blokh, and L. Snoha, Recollections about Sergii Kolyada P. Moree, Sergiy and the MPIM Y. I. Manin and M. Marcolli, Homotopy types and geometries below ${\rm Spec}(\mathbb{Z})$ A. Fel'shtyn and M. Zietek, Dynamical zeta functions of Riedemeister type and representations spaces O. Jenkinson and M. Pollicott, Rigorous dimension estimates for Cantor sets arising in Zaremba theory P. Colognese and M. Pollicott, Volume growth for infinite graphs and translation surfaces J. Byszewski, G. Cornelissen, M. Houben, and L. Van Der Meijden, Dynamically affine maps in positive characteristic S. Kolyada, M. Misiurewicz, and L. Snoha, Special $\alpha$-limit sets E. Shi and X. Ye, Equicontinuity of minimal sets for amenable group actions on dendrites E. Akin, E. Glasner, and B. Weiss, On weak rigidity and weakly mixing enveloping semigroups A. Ganguly and A. Ghosh, The inhomogenous Sprindzhuk conjecture over a local field of positive characteristic A. Blokh, L. Oversteegen, and V. Timorin, Dynamical generation of parameter laminations P. Oprocha, T. Yu, and Guohua Zhang, Multi-sensitivity, multi-transitivity and $\delta$-transitivity R. Sharp, Convergence of zeta functions for amenable group extensions of shifts S. Bezuglyi and O. Karpel, Invariant measures for Cantor dynamical systems M. Kapovich, Periods of abelian differentials and dynamics J. Riedl and D. Schleicher, Crossed renormalization of quadratic polynomials.
£94.50
MP-AMM American Mathematical Tits Polygons
Book Synopsis
£999.99
