- 拓扑流形引论(第2版)(英文版)
- - 作者：(美)约翰·M.李|责编:刘慧
  - 出版社：世界图书出版公司
  - ISBN：9787519276089
  - 出版日期：2020/07/01
  - 页数：433
- 售价：47.6

内容大纲
本书作者是美国华盛顿大学教授，具有丰富的教学经验，他在华盛顿大学和哈佛大学教授流形课程已有15年之久。书中论述了流形理论中所需的拓扑学基本概念，特别是微分几何、代数几何和相关领域。线和曲面；同伦和基本群论；圆和球；群论；Seifert-Van Kampen定理；覆盖空间；覆盖类别；同调。
作者介绍
目录
Preface
1  Introduction
  What Are Manifolds
  Why Study Manifolds
2  Topological Spaces
  Topologies
  Convergence and Continuity
  Hausdorff Spaces
  Bases and Countability
  Manifolds
  Problems
3  New Spaces from Old
  Subspaces
  Product Spaces
  Disjoint Union Spaces
  Quotient Spaces
  Adjunction Spaces
  Topological Groups and Group Actions
  Problems
4  Connectedness and Compactness
  Connectedness
  Compactness
  Local Compactness
  Paracompactness
  Proper Maps
  Problems
5  Cell Complexes
  Cell Complexes and CW Complexes
  Topological Properties of Cw Complexes
  Classification of 1-Dimensional Manifold
  Simplicial Complexes
  Problems
6  Compact Surfaces
  Surfaces
  Connected Sums of Surfaces
  Polygonal Presentations of Surfaces
  The Classification Theorem
  The Euler Characteristic
  Orientability
  Problems
7  Homotopy and the Fundamental Group
  Homotopy
  The Fundamental Group
  Homomorphisms Induced by Continuous Maps
  Homotopy Equivalence
  Higher Homotopy Groups
  Categories and Functors
  Problems
8  The Circle
  Lifting Properties of the Circle

  The Fundamental Group of the Circle
  Degree Theory for the Circle
  Problems
9  Some Group Theory
  Free Products
  Free Groups
  Presentations of Groups
  Free Abelian Groups
  Problems
10  The Seifert-Van Kampen Theorem
  Statement of the Theorem
  Applications
  Fundamental Groups of Compact Surfaces
  Proof of the Seifert-Van Kampen Theorem
  Problems
11  Covering Maps
  Definitions and Basic Properties
  The General Lifting Problem
  The Monodromy Action
  Covering Homomorphisms
  The Universal Covering Space
  Problems
12  Group Actions and Covering Maps
  The Automorphism Group of a Covering
  Ouotients by Group Actions
  The Classification Theorem
  Proper Group Actions
  Problems
13  Homology
  Singular Homology Groups
  Homotopy Invariance
  Homology and the Fundamental Grour
  The Mayer-Vietoris Theorem
  Homology of Spheres
  Homology of CW Complexes
  Cohomology
  Problems
Appendix A: Review of Set Theory
  Basic Concepts
  Cartesian Products,Relations,and Functions
  Number Systems and Cardinality
  Indexed Families
Appendix B: Review of Metric Spaces
  Euclidean Spaces
  Metrics
  Continuity and Convergence
Appendix C: Review of Group Theory
  Basic Definitions
  Cosets and Quotient Groups
  Cyclic Groups

References
Notation Index
Subject Index

内容大纲

作者介绍

目录

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