Andreas Kriegl, Peter W. Michor
Regular infinite dimensional Lie groups
The paper is published: J. Lie Theory, 7,1 (1997), 61--99

MSC:

22E65 Infinite-dimensional Lie groups and their Lie algebras, See also {17B65, 58B25, 58H05}

58B25 Group structures and generalizations on infinite-dimensional manifolds, See also {22E65, 58D05}

53C05 Connections, general theory

Abstract: Regular Lie groups are infinite dimensional Lie groups with the
property that smooth curves in the Lie algebra integrate to
smooth curves in the group in a smooth way (an `evolution operator'
exists). Up to now all known smooth Lie groups are regular.
We show in this paper that
regular Lie groups allow to push surprisingly far the geometry of
principal bundles: parallel transport exists and flat connections
integrate to horizontal foliations as in finite dimensions.
As consequences we obtain that Lie algebra homomorphisms intergrate
to Lie group homomorphisms, if the source group is simply connected
and the image group is regular.

Keywords: Regular Lie groups, infinite dimensional Lie groups, diffeomorphism groups
Notes: J. Lie Theory, 7,1 (1997), 61--99,
ESI Preprint 200.
MR 98k:22081, Z 970.32707,
math.DG/9801007