
Connections, Definite Forms, and Four-Manifolds
Clarendon Press
Published on 31. January 1991
Book
Hardback
142 pages
978-0-19-853599-7 (ISBN)
Description
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.
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.
Reviews / Votes
'For topologists it might be the easiest way into parts of the theory which was started by Donaldson.'P. Michor, Moatshefte fuer Mathematik, Vol. 112, 1991, No. 3
More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Oxford University Press
Target group
College/higher education
Professional and scholarly
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 12 mm
Weight
385 gr
ISBN-13
978-0-19-853599-7 (9780198535997)
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Schweitzer Classification
Persons
Author
Professors, Department of MathematicsProfessors, Department of Mathematics, Rutgers University, New Brunswick, New Jersey
Content
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.