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 There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions.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

Notes

Bibliographic Level Mode of Issuance: Monograph

Source of description

Description based on print version record.

Language note

English

Contents

Handlebodies and framed links

Intersection forms

Classification theorems

Spin structures

T Lie 3 and

Immersing 4-manifolds in R 6

3-Manifolds; a digression

Bounding 5-manifolds

p 1(M) = 3?(M), ? 4 so = Z and ? 4 spin = Z

Wall's diffeomorphisms and H-cobordism

Rohlin's theorem

Casson handles

Freedman's work

Exotic R 4's.

ISBN

3-540-46171-X

OCLC

1066185838

Doi

10.1007/BFb0089031

Statement on language in description

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