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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
ISBN：
978-7-04-063236-1
版面字数：
953.00千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2025-02-07
物料号：
63236-00
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
  • 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

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