Connections, path liftings and Ambrose-Singer theorem on diffeological bundles

Details Connections, path liftings and Ambrose-Singer theorem on diffeological bundles Connections, path liftings and Ambrose-Singer theorem on diffeological bundles

2010-07-21

arxiv.org/abs/1007.3543v1

Mathematics

Differential Geometry

Scientific paper

We develop here the notion of path-liftings, a generalization of horizontal lifts of paths to diffeological bundles for which the holonomy of a loop is well-defined. Then, we link it with the notion of connection on a diffeological bundle with regular Fr\"olicher Lie group. After the statement of technical results and of a Lie theorem for subalgebras of Fr\"olicher subalgebras, we state a reduction theorem and an Ambrose-Singer theorem for a class of diffeological bundles with regular Fr\"olicher Lie groups. The case of (classical) principal bundles with structure group a Lie group $G$ modeled on a locally convex complete topological vector space appears as a particular case.

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