代数拓扑导论 内容简介

本书内容包括：两维流形、基本群体、免费论坛和免费产品的论坛、涵盖空间、基本群体和覆盖空间图、基本群体高维空间等。

代数拓扑导论 本书特色

This textbook is designed to introduce advanced undergraduate or beginning graduate students to algebraic topology as painlessly as possible. The principal topics treated are 2-dimensional manifolds, the fundamental group, and covering spaces, plus the group theory needed in these topics. The only prerequisites are some group theory, such as that normally contained in an undergraduate algebra course on the junior-senior level, and a one-semester undergraduate course in general topology.

代数拓扑导论 目录

CHAPTERONE Two-Dimensional Manifolds
1Introduction
2Definition and examples of n-manifolds
3Orientable vs. nonorientable manifolds
4Examples of compact, connected 2-manifolds
5Statement of the classification theorem for compact surfaces
6Triangulations of compact surfaces
7Proof of Theorem 5.1
8The Euler characteristic of a surface
9Manifolds with boundary
10The classification of compact, connected 2-manifoldswith boundary
11The Euler characteristic of a bordered surface
12Models of compact bordered surfaces in Euclidean 3-space
13Remarks on noncompact surfaces
CHAPTER TWO The Fundamental Group
1Introduction
2Basic notation and terminology
3Definition of the fundamental group of a space
4The effect of a continuous mapping on the fundamental group
5The fundamental group of a circle is infinite cyelic
6Application: The Brouwer fixed-point theorem in dimension 2
7The fundamental group of a product space
8Homotopy type and homotopy equivalence of spaces
CHAPTER THREE Free Groups and Free Products of Groups
1Introduction
2The weak product of abelian groups
3Free abelian groups
4Free products of groups
5Free groups
6The presentation of groups by generators and relations
7Universal mapping problems
CHAPTERFOUR Seifert and Van Kampen Theorem on the Fundamental Group of the Union of Two Spaces.Applica tions
1Introduction
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