4维流形与Kirby演算（影印版）

样章

作者：

Robert E. Gompf，András I. Stipsicz

定价：

199.00 元

版面字数：

953千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2025年

ISBN：

978-7-04-063236-1

物料号：

63236-00

出版时间：

2025-02-07

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

拓扑学

暂无

目录
- 前辅文
- Preface
- Part 1. 4-Manifolds
  - Chapter 1. Introduction
    - §1.1. Manifolds
    - §1.2. 4-manifolds
    - §1.3. Examples
    - §1.4. Appendix
  - Chapter 2. Surfaces in 4-manifolds
    - §2.1. Surfaces in CP2
    - §2.2. The blow-up process
    - §2.3. Desingularization of curves
    - §2.4. Appendix: Introduction to gauge theory
  - Chapter 3. Complex surfaces
    - §3.1. E(1) and fiber sum
    - §3.2. Other constructions of elliptic fibrations
    - §3.3. Logarithmic transformation
    - §3.4. Classification of complex surfaces
- Part 2. Kirby Calculus
  - Chapter 4. Handlebodies and Kirby diagrams
    - §4.1. Handles
    - §4.2. Handle decompositions
    - §4.3. Dimension three — Heegaard splittings
    - §4.4. Dimension four — Kirby diagrams
    - §4.5. Linking numbers and framings
    - §4.6. Examples
  - Chapter 5. Kirby calculus
    - §5.1. Handle moves
    - §5.2. Surgery
    - §5.3. Dehn surgery
    - §5.4. 1-handles revisited
    - §5.5. Relative Kirby calculus
    - §5.6. Spin structures
    - §5.7. Spin structures in Kirby diagrams
  - Chapter 6. More examples
    - §6.1. Plumbings and related constructions
    - §6.2. Embedded surfaces and their complements
    - §6.3. Branched covers
- Part 3. Applications
  - Chapter 7. Branched covers and resolutions
    - §7.1. Definitions and examples
    - §7.2. Resolution of singularities
    - §7.3. Elliptic surfaces revisited
    - §7.4. Surfaces of general type
  - Chapter 8. Elliptic and Lefschetz fibrations
    - §8.1. Lefschetz pencils and fibrations
    - §8.2. The topology of Lefschetz fibrations
    - §8.3. The topology of elliptic surfaces
    - §8.4. Higher genus and generalized fibrations
    - §8.5. Rationally blowing down
  - Chapter 9. Cobordisms, h-cobordisms and exotic R4’s
    - §9.1. Cobordism groups
    - §9.2. h-cobordisms
    - §9.3. Akbulut corks and exotic R4’s
    - §9.4. More exotica
  - Chapter 10. Symplectic 4-manifolds
    - §10.1. Symplectic and almost-complex manifolds
    - §10.2. Constructions of symplectic manifolds
    - §10.3. 4-manifolds with no symplectic structure
    - §10.4. Gauge theory on symplectic 4-manifolds
  - Chapter 11. Stein surfaces
    - §11.1. Contact structures
    - §11.2. Kirby diagrams of Stein surfaces
    - §11.3. Invariants of Stein and contact structures
    - §11.4. Stein surfaces and gauge theory
- Part 4. Appendices
  - Chapter 12. Solutions
    - §12.1. Solutions of some exercises in Part 1
    - §12.2. Solutions of some exercises in Part 2
    - §12.3. Solutions of some exercises in Part 3
  - Chapter 13. Notation, important figures
    - §13.1. List of commonly used notation
    - §13.2. Index of important diagrams
    - §13.3. Index of Kirby moves and related operations
- Bibliography
- Index