Kirby, Robion C.
The Topology of 4-Manifolds [electronic resource] / by Robion C. Kirby. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1989. - VIII, 112 p. online resource. - Lecture Notes in Mathematics, 1374 0075-8434 ; . - Lecture Notes in Mathematics, 1374 .
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 There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions.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.
9783540461715
10.1007/BFb0089031 doi
Mathematics.
Cell aggregation--Mathematics.
Mathematics.
Manifolds and Cell Complexes (incl. Diff.Topology).
QA613-613.8 QA613.6-613.66
514.34
The Topology of 4-Manifolds [electronic resource] / by Robion C. Kirby. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1989. - VIII, 112 p. online resource. - Lecture Notes in Mathematics, 1374 0075-8434 ; . - Lecture Notes in Mathematics, 1374 .
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.
9783540461715
10.1007/BFb0089031 doi
Mathematics.
Cell aggregation--Mathematics.
Mathematics.
Manifolds and Cell Complexes (incl. Diff.Topology).
QA613-613.8 QA613.6-613.66
514.34