Structure groups and holonomy in infinite dimensions
Copyright policy )Structure groups and holonomy in infinite dimensions
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.
15 pages, no figure
Mathematics - Differential Geometry, Mathematics(all), Ambrose-Singer Theorem, Group structures and generalizations on infinite-dimensional manifolds, 58B99, Infinite-dimensional Lie groups and their Lie algebras: general properties, connection, structure group, principal bundle, 58B99; 53C29, 53C29, Differential Geometry (math.DG), Holonomy, curvature, FOS: Mathematics, holonomy, Infinite dimensional Lie groups, Ambrose–Singer theorem, infinite-dimensional Lie group, Connections (general theory)
Mathematics - Differential Geometry, Mathematics(all), Ambrose-Singer Theorem, Group structures and generalizations on infinite-dimensional manifolds, 58B99, Infinite-dimensional Lie groups and their Lie algebras: general properties, connection, structure group, principal bundle, 58B99; 53C29, 53C29, Differential Geometry (math.DG), Holonomy, curvature, FOS: Mathematics, holonomy, Infinite dimensional Lie groups, Ambrose–Singer theorem, infinite-dimensional Lie group, Connections (general theory)
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