Compactness Theorems for Invariant Connections
Abstract
Necessary and sufficient conditions are given for the Palais-Smale Condition C to hold for the Yang-Mills functional for connections that are invariant under a Lie group action on the manifold with orbits of codimension less than or equal to three. As an application the mountain pass lemma is used to give a simple proof of Wang's theorem on the existence of irreducible non-(anti-)selfdual instantons on S2 x S2 .
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