Deformations of groups of gauge transformations

Abstract

This article is concerned with the deformation theory of representations of a given group H into the group of gauge transformations of a principal G-bundle over a manifold X. We develop for gauge groups an analog of André Weil's theory of deformations of representations of finitely generated groups into Lie groups. Explicit computations of the infinitesimal deformations and the associated higher cohomology are made. We extend the Weil theory to treat infinitesimal deformations arising from vector fields on the base manifold and examine the role played by the continuous cohomology of the gauge group.