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Algebraic Topologyby C R F Maunder
Synopses & ReviewsPublisher Comments:Based on lectures to advanced undergraduate and firstyear graduate students, this is a thorough, sophisticated and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. The presentation of the homotopy theory and the account of duality in homology manifolds make the text ideal for a course on either homotopy or homology theory. The idea of algebraic topology is to translate problems in topology into problems in algebra with the hope that they have a better chance of solution. The translation process is usually carried out by means of the homology or homotopy groups of a topological space. Much of the book is therefore concerned with the construction of these algebraic invariants, and with applications to topological problems, such as the classification of surfaces and duality theorems for manifolds. Other important topics covered are homotopy theory, CWcomplexes and the cohomology groups associated with a general Ωspectrum. Dr. Maunder has provided many examples and exercises as an aid, and the notes and references at the end of each chapter trace the historical development of the subject and also point the way to more advanced results. "Throughout the text the style of writing is first class. The author has given much attention to detail, yet ensures that the reader knows where he is going. An excellent book." — Bulletin of the Institute of Mathematics and Its Applications. Synopsis:Thorough, modern treatment, essentially from a homotopy theoretic viewpoint. Topics include homotopy and simplicial complexes, the fundamental group, homology theory, homotopy theory, homotopy groups and CWComplexes, and other topics. Includes exercises. Bibliography. 1980 corrected edition. Synopsis:Thorough, modern treatment, essentially from a homotopy theoretic viewpoint. Topics include homotopy and simplicial complexes, the fundamental group, homology theory, homotopy theory, homotopy groups and CWComplexes and other topics. Each chapter contains exercises and suggestions for further readi
Synopsis:Based on lectures to advanced undergraduate and firstyear graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject.
Table of ContentsCHAPTER 1 ALGEBRAIC AND TOPOLOGICAL PRELIMINARIES
1.1 Introduction 1.2 Set theory 1.3 Algebra 1.4 Analytic Topology CHAPTER 2 HOMOTOPY AND SIMPLICIAL COMPLEXES 2.1 Introduction 2.2 The classification problem; homotopy 2.3 Simplicial complexes 2.4 Homotopy and homeomorphism of polyhedra 2.5 Subdivision and the Simplicial Approximation Theorem Exercises Notes on Chapter 2 CHAPTER 3 THE FUNDAMENTAL GROUP 3.1 Introduction 3.2 Definition and elementary properties of the fundamental group 3.3 Methods of calculation 3.4 Classification of triangulable 2manifolds Exercises Notes on Chapter 3 CHAPTER 4 HOMOLOGY THEORY 4.1 Introduction 4.2 Homology groups 4.3 Methods of calculation: simplicial homology 4.4 Methods of calculation: exact sequences 4.5 "Homology groups with arbitrary coefficients, and the Lefschetz FixedPoint Theorem" Exercises Notes on Chapter 4 CHAPTER 5 COHOMOLOGY AND DUALITY THEOREMS 5.1 Introduction 5.2 Definitions and calculation theorems 5.3 The AlexanderPoincaré Duality Theorem 5.4 Manifolds with boundary and the Lefschetz Duality Theorem Exercises Notes on Chapter 5 CHAPTER 6 GENERAL HOMOTOPY THEORY 6.1 Introduction 6.2 Some geometric constructions 6.3 Homotopy classes of maps 6.4 Exact sequences 6.5 Fibre and cofibre maps Exercises Notes on Chapter 6 CHAPTER 7 HOMOTOPY GROUPS AND CWCOMPLEXES 7.1 Introduction 7.2 Homotopy groups 7.3 CWcomplexes 7.4 Homotopy groups of CWcomplexes 7.5 The theorem of J. H. C. Whitehead and the Cellular Approximation Theorem Exercises Notes on Chapter 7 CHAPTER 8 HOMOLOGY AND COHOMOLOGY OF CWCOMPLEXES 8.1 Introduction 8.2 The Excision Theorem and cellular homology 8.3 The Hurewicz theorem 8.4 Cohomology and EilenbergMacLane spaces 8.5 Products Exercises Notes on Chapter 8 References Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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