Structure groups and holonomy in infinite dimensions

Details Structure groups and holonomy in infinite dimensions Structure groups and holonomy in infinite dimensions

2002-12-11

arxiv.org/abs/math/0212160v1

Bull. Sci. Math. 128 (2004) 513-529

Mathematics

Differential Geometry

15 pages, no figure

Scientific paper

In this article, we give a theorem of reduction of the structure group of a principal bundle P with regular structure group G. Then, when G is in the classes of Lie groups defined by T.Robart [13], we define the closed holonomy group of a connection as the minimal closed Lie subgroup of G for which the previous theorem of reduction can be applied. We also prove an infinite dimensional version of the Ambrose-Singer theorem: the Lie algebra of the holonomy group is spanned by the curvature elements.

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