The Topology of 4-Manifolds [electronic resource] / by Robion C. Kirby.
Material type: TextSeries: Nankai Institute of Mathematics, Tianjin, P.R. China ; 1374Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1989Description: VIII, 112 p. online resourceContent type:- text
- computer
- online resource
- 9783540461715
- 514.34 23
- QA613-613.8
- QA613.6-613.66
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.
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 There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions.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.
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