Compactness Theorems for Invariant Connections

2000/04/07 by Johan Råde, Rade, Johan
Mathematics · #58E15 (Primary) 81T13 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0004041

openalex publication_date 2000/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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