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.
'For topologists it might be the easiest way into parts of the theory which was started by Donaldson.'
P. Michor, Moatshefte für Mathematik, Vol. 112, 1991, No. 3
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.
Series: Oxford Mathematical Monographs
Number Of Pages: 132
Published: 31st January 1991
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 23.8 x 16.3
Weight (kg): 0.45