The Topology Of 4-Manifolds

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 pro...

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Bibliographic Details
Main Author Kirby, Robion C
Format eBook
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin / Heidelberg 2006
Springer Berlin Heidelberg
Springer
Edition1
SeriesNankai Institute of Mathematics, Tianjin, P.R. China
Subjects
Cell aggregation
Dimensional analysis
Manifolds and Cell Complexes (incl. Diff.Topology)
Mathematics
Mathematics and Statistics
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Summary: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 There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions.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.
ISBN:3540511482
9783540511489
3662162741
9783662162743
ISSN:0075-8434
1617-9692
DOI:10.1007/BFb0089031