The Topology of 4-Manifolds

1989
ISBN: 978-3-540-51148-9
Verlag: Springer

Buch, Englisch, Band 1374, 112 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 195 g

Reihe: Lecture Notes in Mathematics

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 There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions.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

Zielgruppe

Research

Autoren/Hrsg.

Kirby, Robion C.

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

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.