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Gauge theory and fibre symmetries. (Théorie de jauge et symétries de fibrés.) (French) Zbl 0778.57018
Soit \(\xi\) un \(G\)-fibré principal différentiable sur une variété \(M\) (\(G\) un groupe de Lie compact). Etant donné une action d’un groupe de Lie compact \(\Gamma\) sur \(M\), on se pose la question de savoir si elle provient d’une action sur le fibré \(\xi\). L’originalité de ce travail est de relier ce problème à l’existence de points fixes pour les actions de \(\Gamma\) que l’on induit naturellement sur divers espaces de modules de \(G\)-connexions sur \(\xi\).
Reviewer: D.Brandt (Geneve)

MSC:
57S15 Compact Lie groups of differentiable transformations
55R10 Fiber bundles in algebraic topology
53C05 Connections, general theory
58D29 Moduli problems for topological structures
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