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拓扑流形引论PDF|Epub|txt|kindle电子书版本网盘下载
- John M.Lee著 著
- 出版社： 北京;西安：世界图书出版公司
- ISBN：7506259591
- 出版时间：2003
- 标注页数：385页
- 文件大小：59MB
- 文件页数：405页
- 主题词：
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图书目录
1 Introduction1
What Are Manifolds？1
Why Study Manifolds？4
2 Topological Spaces17
Topologies17
Bases27
Manifolds30
Problems36
3 New Spaces from Old39
Subspaces39
Product Spaces48
Quotient Spaces52
Group Actions58
Problems62
4 Connectedness and Compactness65
Connectedness65
Compactness73
Locally Compact Hausdorff Spaces81
Problems88
5 Simplicial Complexes91
Euclidean Simplicial Complexes92
Abstract Simplicial Complexes96
Triangulation Theorems102
Orientations105
Combinatorial Invariants109
Problems114
6 Curves and Surfaces117
Classification of Curves118
Surfaces119
Connected Sums126
Polygonal Presentations of Surfaces129
Classification of Surface Presentations137
Combinatorial Invariants142
Problems146
7 Homotopy and the Fundamental Group147
Homotopy148
The Fundamental Group150
Homomorphisms Induced by Continuous Maps158
Homotopy Equivalence161
Higher Homotopy Groups169
Categories and Functors170
Problems176
8 Circles and Spheres179
The Fundamental Group of the Circle180
Proofs of the Lifting Lemmas183
Fundamental Groups of Spheres187
Fundamental Groups of Product Spaces188
Fundamental Groups of Manifolds189
Problems191
9 Some Group Theory193
Free Products193
Free Groups199
Presentations of Groups201
Free Abelian Groups203
Problems208
10 The Seifert-Van Kampen Theorem209
Statement of the Theorem210
Applications212
Proof of the Theorem221
Distinguishing Manifolds227
Problems230
11 Covering Spaces233
Definitions and Basic Properties234
Covering Maps and the Fundamental Group239
The Covering Group247
Problems253
12 Classification of Coverings257
Covering Homomorphisms258
The Universal Covering Space261
Proper Group Actions266
The Classification Theorem283
Problems289
13 Homology291
Singular Homology Groups292
Homotopy Invariance300
Homology and the Fundamental Group304
The Mayer-Vietoris Theorem308
Applications318
The Homology of a Simplicial Complex323
Cohomology329
Problems334
Appendix：Review of Prerequisites337
Set Theory337
Metric Spaces347
Group Theory352
References359
Index362