Description
Book SynopsisOffers a panorama of the topology of simply connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but small enough so that there is no room to undo the wildness.
Trade ReviewThe book gives an excellent overview of 4-manifolds, with many figures and historical notes. Graduate students, nonexperts, and experts alike will enjoy browsing through it. -- Robion C. Kirby, University of California, Berkeley What a wonderful book! I strongly recommend this book to anyone, especially graduate students, interested in getting a sense of 4-manifolds."" —
MAA Reviews""The author records many spectacular results in the subject ... (the author) gives the reader a taste of the techniques involved in the proofs, geometric topology, gauge theory and complex and symplectic structures. The book has a large and up-to-date collection of references for the reader wishing to get a more detailed or rigorous knowledge of a specific topic. The exposition is user-friendly, with a large number of illustrations and examples."" —
Mathematical ReviewsTable of Contents
- Introduction
- Front matter
- Part I: Background scenery: Introduction
- Contents of part I
- Chapter 1: Higher dimensions and the $h$-cobordism theorem
- Chapter 2: Topological 4-manifolds and $h$-cobordisms
- Part II: Smooth 4-manifolds and intersection forms: Introduction
- Contents of part II
- Chapter 3: Getting acquainted with intersection forms
- Chapter 4: Intersection forms and topology
- Chapter 5: Classifications and counterclassifications
- Part III: A survey of complex surfaces: Introduction
- Contents of part III
- Chapter 6: Running through complex geometry
- Chapter 7: The Enriques-Kodaira classification
- Chapter 8: Elliptic surfaces
- Part IV: Gauge theory on 4-manifolds: Introduction
- Contents of part IV
- Chapter 9: Prelude, and the Donaldson invariants
- Chapter 10: The Seiberg-Witten invariants
- Chapter 11: The minimum genus of embedded surfaces
- Chapter 12: Wildness unleashed: The Fintushel-Stern surgery
- Epilogue
- List of figures and tables
- Bibliography
- Index
- Errata
