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.
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