A Compactness Theorem for Invariant Connections

Abstract

Necessary and sufficient conditions are given for the Palais-Smale Condition C to hold for the Yang-Mills functional for invariant connections on a principal bundle over a compact manifold of any dimension. It is assumed that the connections are invariant under the action of a compact Lie group on the manifold, and that all orbits of the action have codimension three or less.

25 pages, plain TeX. Revised version: the paper has been reorganized, some minor errors have been corrected, more examples have been added

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