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 There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions.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

List of 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.

Product details

• Authors: Robin C. Kirby, Robion C Kirby, Robion C. Kirby
• Publisher: Springer, Berlin
• Languages: English, German
• Product format: Paperback / Softback
• Released: 26.06.2009
• EAN: 9783540511489
• ISBN: 978-3-540-51148-9
• No. of pages: 112
• Dimensions: 156 mm x 236 mm x 8 mm
• Weight: 200 g
• Illustrations: VIII, 112 p.
• Series: Lecture Notes in Mathematics / Nankai Institute of Mathematics, Tianjin, P.R. China; Lecture Notes in Mathematics; Lecture Notes in Mathematics / Nankai Institute of Mathematics, Tianjin, P.R. China; Nankai Institute of Mathematics, Tianjin, P.R. China
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Geometry