The Topology of 4-Manifolds / Edition 1

by Robion C. Kirby

Overview

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 There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions.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

Product Details

ISBN-13:	9783540511489
Publisher:	Springer Berlin Heidelberg
Publication date:	07/18/1995
Series:	Lecture Notes in Mathematics , #1374
Edition description:	1989
Pages:	112
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table 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.