基本信息

书名:代数拓扑导论

定价：50.00元

作者:(美)罗曼　著

出版社：世界图书出版公司

出版日期：2009_08_01

ISBN：9787506282802

字数：

页码：

版次：1

装帧：平装

开本：24开

商品重量：

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内容提要

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
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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