出版社：世界图书出版公司北京公司
年代：2009
定价：52.0
本书清晰地阐述了代数拓扑的基本思想，并配有大量练习。内容包括：奇异同调、单纯同调及胞腔同调；同伦群及上同调环。
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 Greens 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
Chain Equivalences
Acyclic Models
Lefschetz Fixed Point Theorem
Tensor Products
Universal Coefficients
Eilcnberg-Zilber Theorem and the Kunneth Formula
CHAPTER 10
Covering Spaces
Basic Properties
Covering Transformations
Existence
Orbit Spaces
CHAPTER 11
Homotopy Groups
Function Spaces
Group Objects and Cogroup Objects
Loop Space and Suspension
Homotopy Groups
Exact SequenCes
Fihrations
A Glimpse Ahead
CHAPTER 12
Cohomology
Differential Forms
Cohomology Groups
Universal Coefficients Theorems for Cohomology
Cohomology Rings
Computations and Applications
Bibliography
Notation
Index
There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to .I.H.C. Whitehead. Of course， this is false， as a giance at the books of Hilton and Wylie， Maunder， Munkres， and Schubert reveals. Still， the canard does reflect some truth. Too often one finds too much generality and too little attention to details.
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| 书名 | 代数拓扑导论站内查询相似图书 | ||
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| 出版地 | 北京 | 出版单位 | 世界图书出版公司北京公司 |
| 版次 | 1版 | 印次 | 1 |
| 定价(元) | 52.0 | 语种 | 英文 |
| 尺寸 | 14 | 装帧 | 平装 |
| 页数 | 印数 | 1000 | |
代数拓扑导论是世界图书出版公司北京公司于2009.08出版的中图分类号为 O189.2 的主题关于 代数拓扑－英文 的书籍。