代数拓扑（影印版）|天元基金影印系列丛书|（美）Allen Hatcher|清华大学出版社

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代数拓扑（影印版）

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原书名：Algebraic Topology	原出版社：Cambridge University Press
作者：（美）Allen Hatcher	出版社：清华大学出版社
译者：	丛书名：天元基金影印系列丛书
出版日期：2005-3-1	上架日期：2005-10-8
ISBN：730210588X	页数：版次：1-1
开本：185×230	装帧：

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内容简介
This geometrically flavored introduction to algebraic topology has the dual goals of serving as a textbook for a standard graduate-level course and as a background reference for many additional topics that do not usually fit into such a course. The broad cover-age includes both the homological and homotopical sides of the subject. Care has been taken to present a readable, self-contained exposition, with many examples and exercises, aimed at the student or the researcher from another area of mathematics seeing the subject for the first time.
The four main chapters present the basic core material of algebraic topology: fundamental groups, homology, cohomology, and higher homotopy groups. Each chapter concludes with a generous selection of optional topics, accounting for nearly half the book altogether.

目录
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Preface
Standard Notations xii.
Chapter O. Some Underlying Geometric Notions
Homotopy and Homotopy Type 1. Cell Complexes 5.
Operations on Spaces 8. Two Criteria for Homotopy Equivalence 10.
The Homotopy Extension Property 14.
Chapter 1. The Fundamental Group
1.1. Basic Constructions
Paths and Homotopy 25. The Fundamental Group of the Circle 29.
Induced Homomorphisms 34.
1.2. Van Kampen's Theorem
Free Products of Groups 41. The van Kampen Theorem 43.
Applications to Cell Complexes 50.
1.3. Covering Spaces
Lifting Properties 60. The Classification of Covering Spaces 63.
Deck Transformations and Group Actions 70.
Additional Topics
1.A. Graphs and Free Groups 83.
1.B. K(G,1) Spaces and Graphs of Groups 87.
Chapter 2. Homology
2.1. Simplicial and Singular Homology
A-Complexes 102. Simplicial Homology 104. Singular Homology 108.
Homotopy Invariance 110. Exact Sequences and Excision 113.
The Equivalence of Simplicial and Singular Homology 128.
2.2. Computations and Applications
Degree 134. Celluiar Homology 137. Mayer-Vietoris Sequences 149.
Homology with Coefficients 153.
2.3. The Formal Viewpoint
Axioms for Homology 160. Categories and Functors 162.
Additional Topics
2.A. Homology and Fundamental Group 166.
2.B. Classical Applications 169.
2.C. Simplicial Approximation 177.
Chapter 3. Cohomology
3.1. Cohomology Groups
The Universal Coefficient Theorem 190. Cohomology of Spaces 197.
3.2. Cup Product
The Cohomology Ring 211. A Kunneth Formula 218.
Spaces with Polynomial Cohomology 224.
3.3. Poincare Duality
Orientations and Homology 233. The Duality Theorem 239,
Connection with Cup Product 249. Other Forms of Duality 252.
Additional Topics
3.A. Universal Coefficients for Homology 261.
3.B. The General Kunneth Formula 268.
3.C. H-Spaces and Hopf Algebras 281.
3.D. The Cohomology of SO(n) 292.
3.E. Bockstein Homomorphisms 303.
3.F. Limits and Ext 311.
3.G. Transfer Homomorphisms 321.
3.H. Local Coefficients 327.
Chapter 4. Homotopy Theory
4.1. Homotopy Groups
Definitions and Basic Constructions 340. Whitehead's Theorem 346.
Cellular Approximation 348. CW Approximation 352.
4.2. Elementary Methods of Calculation
Excision for Homotopy Groups 360. The Hurewicz Theorem 366.
Fiber Bundles 375. Stable Homotopy Groups 384.
4.3. Connections with Cohomology
The Homotopy Construction of Cohomology 393. Fibrations 405.
Posmikov Towers 410. Obstruction Theory 415.
Additional Topics
4.A. Basepoints and Homotopy 421.
4.B. The Hopf Invariant 427.
4.C. Minimal Ce]] Structures 429.
4.D. Cohomology of Fiber Bundles 431.
4.E. The Brown Representability Theorem 448.
4.F. Spectra and Homology Theories 452.
4.G. Gluing Constructions 456.
4.H. Eckmann-Hilton Duality 460.
4.I. Stable Splittings of Spaces 466.
4.J. The Loopspace of a Suspension 470.
4.K. The Dold-Thom Theorem 475.
4.L. Steenrod Squares and Powers 487.
Appendix
Topology of Cell Complexes 519. The Compact-Open Topology 529.
Bibliography
Index

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读者：scubookworm 最新讨论：2006-2-18 11:47:26 评价等级：
此书是近年美国流行的代数拓扑教材。无论是内容还是形式都相当不错，习题活泼多变，看完Munkres的《Topology》后，跟着看本书，相信你的拓扑功底就不错了。总的来说，此书堪称新的代数拓扑经典！
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