代数拓扑导论

版次：1
页数：
字数：
印刷时间：2009年08月01日
开本：24开
纸张：胶版纸
包装：平装
是否套装：否
国际标准书号ISBN：9787506282802
作者:（美）罗曼　著出版社:世界图书出版公司出版时间:2009年08月

目　　录

Preface
To the Reader
CHAPTER 0 Introduction
Notation
Brouwer Fixed Point Theorem
Categories and Functors
CHAPTER 1 Some Basic Topological Notions
Homotopy
Convexity, Contractibility, and Cones
Paths and Path Connectedness
CHAPTER 2 Simplexes
Affine Spaces
Aftine Maps
CHAPTER 3 The Fundamental Group

Preface To the Reader CHAPTER 0 Introduction Notation Brouwer Fixed Point Theorem Categories and Functors CHAPTER 1 Some Basic Topological Notions Homotopy Convexity, Contractibility, and Cones Paths and Path Connectedness CHAPTER 2 Simplexes Affine Spaces Aftine Maps CHAPTER 3 The Fundamental Group The Fundamental Groupoid The Functor π π1(S1) CHAPTER 4 Singular Homology Holes and Green's Theorem Free Abelian Groups The Singular Complex and Homology Functors Dimension Axiom and Compact Supports The Homotopy Axiom The Hurewicz Theorem CHAPTER 5 Long Exact Sequences The Category Comp Exact Homology Sequences Reduced Homology CHAPTER 6 Excision and Applications Excision and Mayer-Vietoris Homology of Spheres and Some Applications Barycentric Subdivision and the Proof of Excision Moxe Applications to Euclidean Space CHAPTER 7 Simplicial Complexes Definitions Simplicial Approximation Abstract Simplicial Complexes Simplicial Homology Comparison with Singular Homology Calculations Fundamental Groups of Polyhedra The Seifert-van Kampen Theorem CHAPTER 8 CW Complexes Hausdorff Quotient Spaces Attaching Calls Homology and Attaching Cells CW Complexes Cellular Homology CHAPTER 9 Natural Transformations Definitions and Examples Eilenberg-Steenrod Axioms …… CHAPTER 10 Covering Spaces CHAPTER 11 Homotopy Groups CHPATER 12 Cohomology Bibliography Notation Index

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