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, Walls diffeomorphisms and h-cobordism, and Rohlins 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 Rohlins theorem using spin structures. There is an introduction to Casson handles and Freedmans work including a chapter of unpublished proofs on exotic R4s. 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.