© 1989

The Topology of 4-Manifolds

  • Authors

Part of the Lecture Notes in Mathematics book series (LNM, volume 1374)

Table of contents

  1. Front Matter
    Pages I-VI
  2. Robion C. Kirby
    Pages 1-2
  3. Robion C. Kirby
    Pages 3-19
  4. Robion C. Kirby
    Pages 20-30
  5. Robion C. Kirby
    Pages 31-32
  6. Robion C. Kirby
    Pages 33-37
  7. Robion C. Kirby
    Pages 43-45
  8. Robion C. Kirby
    Pages 46-48
  9. Robion C. Kirby
    Pages 49-56
  10. Robion C. Kirby
    Pages 57-58
  11. Robion C. Kirby
    Pages 59-63
  12. Robion C. Kirby
    Pages 64-71
  13. Robion C. Kirby
    Pages 72-85
  14. Robion C. Kirby
    Pages 86-94
  15. Robion C. Kirby
    Pages 95-101
  16. Back Matter
    Pages 102-108

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 There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions.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


Characteristic class Homotopy diffeomorphism manifold topology

Bibliographic information

  • Book Title The Topology of 4-Manifolds
  • Authors Robion C. Kirby
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lecture Notes in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-51148-9
  • eBook ISBN 978-3-540-46171-5
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages VIII, 112
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Manifolds and Cell Complexes (incl. Diff.Topology)
  • Buy this book on publisher's site