代数拓扑导论

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四川成都

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作者（美）罗曼　著

出版社世界图书出版公司

ISBN9787506282802

出版时间2009-08

装帧平装

开本24开

纸张胶版纸

定价50元

货号20670119

上书时间2024-07-12

已实名已认证进店收藏店铺

商品描述: 【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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