过去的二十年间，四维流形理论经历了爆炸性增长。目前有许多书籍从规范理论或代数几何等不同角度来探讨这一主题。然而，本书提供了一种从拓扑学角度来阐述的方法。它弥合了与其他学科之间的鸿沟，并介绍了经典但重要的拓扑技术，这些技术以前在文献中并未出现过。 本书的第一部分以研究生二年级水平介绍了该理论的基础知识，并概述了当前的研究动向。第二部分专门讲述了Kirby演算，即四维流形上的手柄体理论。这部分内容既基础又全面。 第三部分深入探讨了当前四维流形研究的广泛课题。其中包括分支覆盖和复杂曲面地理学、椭圆和Lefschetz纤维化、h-可边界、辛四维流形和Stein曲面等课题。书中还提供了应用示例，配有300多幅插图和大量习题及解答。 本书以拓扑学的观点展开，向读者介绍了该领域的经典技术，并涵盖了相关研究的最新进展。它对于研究人员和学生们深入理解四维流形理论以及在其他学科中的应用具有重要意义。

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