OXFORD UNIVERSITY PRESS

Connections, Definite Forms and Four-manifolds

ISBN : 9780198535997

Price(incl.tax): 
¥13,332
Author: 
Ted Petrie; John Randall
Pages
142 Pages
Format
Hardcover
Size
163 x 238 mm
Pub date
Jan 1991
Series
Oxford Mathematical Monographs
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The central theme of this book is the study of self-dual connections on four-manifolds. The authors have adopted a topologists' perspective and so have included many of the explicit calculations using the Atiyah-Singer index theorem as well as presenting arguments couched in terms of equivariant topology. The authors' aim is to present moduli space techniques applied to four-manifolds and to study vector bundles over four-manifolds whose structure group is SO(3). Results covered include Donaldson's proof that the only positive definite forms occur as intersection forms and the results 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 an area that is currently one of the most active in mathematical research.

Index: 

Preface
Introduction
Connections
SO(3) - connections
Index of the fundamental complex
The virtual moduli space B
The virtual moduli space M
Intersection forms on 4-manifolds
Moduli space for invariant connections
Applications to homology 3-spheres
Appendices
Bibliography.

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