The Topology of 4-Manifolds

1. Front Matter

   Pages I-VI

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2. Introduction

   • Robion C. Kirby

   Pages 1-2

3. Handlebodies and framed links

   • Robion C. Kirby

   Pages 3-19

4. Intersection forms

   • Robion C. Kirby

   Pages 20-30

5. Classification theorems

   • Robion C. Kirby

   Pages 31-32

6. Spin structures

   • Robion C. Kirby

   Pages 33-37

7. T ³_Lie and \(CP^2 \mathop \sharp \limits^9 ( - CP^2 )\)

   • Robion C. Kirby

   Pages 38-42

8. Immersing 4-manifolds in R ⁶

   • Robion C. Kirby

   Pages 43-45

9. 3-Manifolds; a digression

   • Robion C. Kirby

   Pages 46-48

10. Bounding 5-manifolds

    • Robion C. Kirby

    Pages 49-56

11. p₁(M) = 3σ(M), ω ^so₄ = Z and ω ^spin₄ = Z

    • Robion C. Kirby

    Pages 57-58

12. Wall's diffeomorphisms and H-cobordism

    • Robion C. Kirby

    Pages 59-63

13. Rohlin's theorem

    • Robion C. Kirby

    Pages 64-71

14. Casson handles

    • Robion C. Kirby

    Pages 72-85

15. Freedman's work

    • Robion C. Kirby

    Pages 86-94

16. Exotic R ⁴'s

    • Robion C. Kirby

    Pages 95-101

17. Back Matter

    Pages 102-108

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This book presents the classical theorems about simply connected smooth 4-manifolds: intersection forms and homotopy type, oriented and spin bordism, the index theorem, Wall's diffeomorphisms and h-cobordism, and Rohlin's theorem. Most of the proofs are new or are returbishings of post proofs; all are geometric and make us of handlebody theory. There is a new proof of Rohlin's theorem using spin structures. There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions. The book should be useful to beginning researchers in 4-manifolds.

• Characteristic class
• Homotopy
• diffeomorphism
• manifold
• topology

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