Connections, Definite Forms, and Four-manifolds (Oxford Mathematical Monographs) - Hardcover

Petrie, Ted; Randall, John

Hardcover

ISBN 10: 0198535996 ISBN 13: 9780198535997

Publisher: Clarendon Press, 1991

Synopsis

The central theme of this book is the study of self-dual connections on four-manifolds. The author's aim is to present a lucid introduction to moduli space techniques (for vector bundles with SO (3) as structure group) and to apply them to four-manifolds. The authors have adopted a topologists' perspective. For example, they have included some explicit calculations using the Atiyah-Singer index theorem as well as methods from equivariant topology in the study of the topology of the moduli space. Results covered include Donaldson's Theorem that the only positive definite form which occurs as an intersection form of a smooth four-manifold is the standard positive definite form, as well as those of Fintushel and Stern which show that the integral homology cobordism group of integral homology three-spheres has elements of infinite order. Little previous knowledge of differential geometry is assumed and so postgraduate students and research workers will find this both an accessible and complete introduction to currently one of the most active areas of mathematical research.

About this title

Review:

'For topologists it might be the easiest way into parts of the theory which was started by Donaldson.' P. Michor, Moatshefte fur Mathematik, Vol. 112, 1991, No. 3

About this edition

• Publisher: Clarendon Press
• Publication date: 1991
• ISBN 10: 0198535996
• ISBN 13: 9780198535997
• Binding: Hardcover
• Edition number: 1
• Number of pages: 142