《國外數學名著系列67：拓撲學2》是由科學出版社出版的圖書，作者是諾維科夫。
基本介紹
- 書名：國外數學名著系列67：拓撲學2
- 又名：Topology Ⅱ: Homotopy and Homology, Classical Manifolds
- 作者：諾維科夫
- ISBN：9787030235107
- 頁數：257頁
- 出版社：科學出版社
- 裝幀：精裝
- 開本：16
- 正文語種：英語
- 重量：599 g
內容簡介,目錄,
內容簡介
《國外數學名著系列(續1)(影印版)67:拓撲學2(同倫與同調,經典流形)》主要內容：Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an upto-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmannians and lowdimensional manifolds.
Their book will be used by graduate students and researchers in mathematics and mathematical physics.
目錄
Ⅰ. Introduction to Homotopy Theory
Chapter 1.Basic Concepts
1. Terminology and Notations
1.1. Set Theory
1.2. Logical Equivalence
1.3. Topological Spaces
1.4. Operations on Topological Spaces
1.5. Operations on Pointed Spaces
2. Homotopy
2.1. Homotopies
2.2. Paths
2.3. Homotopy as a Path
2.4. Homotopy Equivalence
2.5. Retractions
2.6. Deformation Retractions
2.7. Relative Homotopies
2.8. k-connectedness
2.9. Borsuk Pairs
2.10. CNRS Spaces
2.11. Homotopy Properties of Topological Constructions
2.12. Natural Group Structures on Sets of Homotopy Classes
3. Homotopy Groups
3.1. Absolute Homotopy Groups
3.2. Digression: Local Systems
3.3. Local Systems of Homotopy Groups of a Topological Space
3.4. Relative Homotopy Groups
3.5. The Homotopy Sequence of a Pair
3.6. Splitting
3.7. The Homotopy Sequence of a Triple
Chapter 2.Bundle Techniques
4. Bundles
4.1. General Definitions
4.2. Locally Trivial Bundles
4.3. Serre Bundles
4.4. Bundles of Spaces of Maps
5. Bundles and Homotopy Groups
5.1. The Local System of Homotopy Groups of the Fibres of a Serre Bundle
5.2. The Homotopy Sequence of a Serre Bundle
5.3. Important Special Cases
6. The Theory of Coverings
6.1. Coverings
6.2. The Group of a Covering
6.3. Hierarchies of Coverings
6.4. The Existence of Coverings
6.5. Automorphisms of a Coveting
6.6. Regular Coverings
6.7. Covering Maps
Chapter 3 Cellular Techniques
7. Cellular Spaces
7.1. Basic Concepts
7.2. Gluing of Cellular Spaces from Balls
7.3. Examples of Cellular Decompositions
7.4. Topological Properties of Cellular Spaces
7.5. Cellular Constructions
8. Simplicial Spaces
8.1. Basic Concepts
8.2. Simplicial Schemes
8.3. Simplicial Constructions
8.4. Stars, Links, Regular Neighbourhoods
8.5. Simplicial Approximation of a Continuous Map
9. Cellular Approximation of Maps and Spaces
9.1. Cellular Approximation of a Continuous Map
9.2. Cellular k-connected Pairs
9.3. Simplicial Approximation of Cellular Spaces
9.4. Weak Homotopy Equivalence
9.5. Cellular Approximation to Topological Spaces
9.6. The Covering Homotopy Theorem
Chapter 4 The Simplest Calculations
10. The Homotopy Groups of Spheres and Classical Manifolds
10.1. Suspension in the Homotopy Groups of Spheres
10.2. The Simplest Homotopy Groups of Spheres
10.3. The Composition Product
10.4. Homotopy Groups of Spheres
10.5. Homotopy Groups of Projective Spaces and Lens Spaces
10.6. Homotopy Groups of the Classical Groups
10.7. Homotopy Groups of Stiefel Manifolds and Spaces
10.8. Homotopy Groups of Grassmann Manifolds and Spaces
11. Application of Cellular Techniques
11.1. Homotopy Groups of a 1-dimensional Cellular Space
11.2. The Effect of Attaching Balls
11.3. The Fundamental Group of a Cellular Space
11.4. Homotopy Groups of Compact Surfaces
11.5. Homotopy Groups of Bouquets
11.6. Homotopy Groups of a k-connected Cellular Pair
11.7. Spaces with Given Homotopy Groups
12. Appendix
12.1. The Whitehead Product
12.2. The Homotopy Sequence of a Triad
12.3. Homotopy Excision, Quotient and Suspension Theorems
