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代数拓扑2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

（美）哈彻（Hatcher，A.）著著
出版社：清华大学出版社
ISBN：730210588X
出版时间：2005
标注页数：544页
文件大小：98MB
文件页数：40075207页
主题词：代数拓扑－研究生－教材－英文

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图书目录

Chapter 0.Some Underlying Geometric Notions1

Homotopy and Homotopy Type1

Cell Complexes5

Operations on Spaces8

Two Criteria for Homotopy Equivalence10

The Homotopy Extension Property14

Chapter 1.The Fundamental Group21

1.1.Basic Constructions25

Paths and Homotopy25

The Fundamental Group of the Circle29

Induced Homomorphisms34

1.2.Van Kampen's Theorem40

Free Products of Groups41

The van Kampen Theorem43

Applications to Cell Complexes50

1.3.Covering Spaces56

Lifting Properties60

The Classification of Covering Spaces63

Deck Transformations and Group Actions70

Additional Topics83

1.A.Graphs and Free Groups83

1.B.K（G,1）Spaces and Graphs of Groups87

Chapter 2.Homology97

2.1.Simplicial and singular Homology102

△-Complexes102

Simplicial Homology104

Singular Homology108

Homotopy Invariance110

Exact Sequences and Excision113

The Equivalence of Simplicial and Singular Homology128

2.2.Computations and Applications134

Degree134

Cellular Homology137

Mayer-Vietoris Sequences149

Homology with Coefficients153

2.3.The Formal Viewpoint160

Axioms for Homology160

Categories and Functors162

Additional Topics166

2.A.Homology and Fundamental Group166

2.B.Classical Applications169

2.C.Simplicial Approximation177

Chapter 3.Cohomology185

3.1.Cohomology Groups190

The Universal Coefficient Theorem190

Cohomology of Spaces197

3.2.Cup Product206

The Cohomology Ring211

A Künneth Formula218

Spaces with Polynomial Cohomology224

3.3.Poincaré Duality230

Orientations and Homology233

The Duality Theorem239

Connection with Cup Product249

Other Forms of Duality252

Additional Topics261

3.A.Universal Coefficients for Homology261

3.B.The General Künneth　Formula268

3.C.H-Spaces and Hopf Algebras281

3.D.The Cohomology of SO（n）292

3.E.Bockstein Homomorphisms303

3.F.Limits and Ext311

3.G.Transfer Homomorphisms321

3.H. Local Coefficients327

Chapter 4.Homotopy Theory337

4.1.Homotopy Groups339

Definitions and Basic Constructions340

Whitehead,s Theorem346

Cellular Approximation348

CW Approximation352

4.2.Elementary Methods of Calculation360

Excision for Homotopy Groups360

The Hurewicz Theorem366

Fiber Bundles375

Stable Homotopy Groups384

4.3.Connections with Cohomology393

The Homotopy Construction of Cohomology393

Fibrations405

Postnikov Towers410

Obstruction Theory415

Additional Topics421

4.A.Basepoints and Homotopy421

4.B.The Hopf Invariant427

4.C.Minimal Cell Structures429

4.D.Cohomology of Fiber Bundles431

4.E.The Brown Representability Theorem448

4.F.Spectra and Homology Theories452

4.G.Gluing Constructions456

4.H.Eckmann-Hilton Duality460

4.I.Stable Splittings of Spaces466

4.J.The Loopspace of a Suspension470

4.K.The Dold-Thom Theorem475

4.L.Steenrod Squares and Powers487

Appendix519

Topology of Cell Complexes519

The Compact-Open Topology529

Bibliography533

Index539