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The Topology of 4-Manifolds

  • Book
  • © 1989

Overview

Authors:
  1. Robion C. Kirby
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1374)

Part of the book sub series: Nankai Institute of Mathematics, Tianjin, P.R. China (2803)

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Table of contents (15 chapters)

  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 3Lie 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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Keywords

About this book

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 There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions.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.

Bibliographic Information

  • Book Title: The Topology of 4-Manifolds

  • Authors: Robion C. Kirby

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0089031

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • Softcover ISBN: 978-3-540-51148-9Published: 10 May 1989

  • eBook ISBN: 978-3-540-46171-5Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 112

  • Topics: Manifolds and Cell Complexes (incl. Diff.Topology)

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