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Fixed points and reducibles in equivariant gauge theory

Fixed points and reducibles in equivariant gauge theory In this paper we prove two technical theorems about the equivariant moduli space of ASD connections on a SU 2 or SO 3 bundle over a smooth oriented four-manifold X which is equipped with a smooth and orientation preserving action of a finite group π. The first theorem relates, in the case π = ℤ/ p and compact moduli spaces, the existence of a non empty fixed set in the moduli space to the value of a certain Donaldson polynomial invariant. The second theorem gives a criterion under which one can avoid fixed reducible ASD connections by slightly varying the metric on X within the class of equivariant metrics. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Fixed points and reducibles in equivariant gauge theory

Weber, Christian
Forum Mathematicum , Volume 10 (5) – Sep 1, 1998
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Publisher
de Gruyter
Copyright
© Walter de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.10.5.605
Publisher site
See Article on Publisher Site

Abstract

In this paper we prove two technical theorems about the equivariant moduli space of ASD connections on a SU 2 or SO 3 bundle over a smooth oriented four-manifold X which is equipped with a smooth and orientation preserving action of a finite group π. The first theorem relates, in the case π = ℤ/ p and compact moduli spaces, the existence of a non empty fixed set in the moduli space to the value of a certain Donaldson polynomial invariant. The second theorem gives a criterion under which one can avoid fixed reducible ASD connections by slightly varying the metric on X within the class of equivariant metrics.

Journal

Forum Mathematicum – de Gruyter

Published: Sep 1, 1998

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