代数拓扑导论
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作者： （美）梅西著
出 版 社：
出版时间： 2009-4-1字数：版次： 1页数： 261印刷时间：开本： 16开印次： 1纸张：I S B N ： 9787510004421包装： 平装目录
CHAPTER ONE Two-Dimensional Manifolds
1 Introduction
2 Definition and examples of n-manifolds
3 Orientable vs. nonorientable manifolds
4 Examples of compact, connected 2-manifolds
5 Statement of the classification theorem for compact surfaces
6 Triangulations of compact surfaces
7 Proof of Theorem 5.1
8 The Euler characteristic of a surface
9 Manifolds with boundary
10 The classification of compact, connected 2-manifolds with boundary
11 The Euler characteristic of a bordered surface
12 Models of compact bordered surfaces in Euclidean 3-space
13 Remarks on noncompact surfaces
CHAPTER TWO The Fundamental Group
1 Introduction
2 Basic notation and terminology
3 Definition of the fundamental group of a space
4 The effect of a continuous mapping on the fundamental group
5 The fundamental group of a circle is infinite cyelic
6 Application: The Brouwer fixed-point theorem in dimension 2
7 The fundamental group of a product space
8 Homotopy type and homotopy equivalence of spaces
CHAPTER THREE Free Groups and Free Products of Groups
1 Introduction
2 The weak product of abelian groups
3 Free abelian groups
4 Free products of groups
5 Free groups
6 The presentation of groups by generators and relations
7 Universal mapping problems
CHAPTER FOUR Seifert and Van Kampen Theorem on the Fundamental Group of the Union of Two Spaces.Applica tions
1 Introduction
2 Statement and proof of the theorem of Seifert and Van Kampen
……
CHAPTER FIVE Covering Spaces
CHAPTER SIX The Fundamental Group and Covering Spaces of a Graph.Applications to Group Theory
CHAPTER SEVEN The Fundamental Group of Higher Dimensional Spaces
CHAPTER EIGHT Epilogue
APPENDIX A The Quotient Space or Identification Space Topology
Permutation Groups or Transformation Groups
Index
