An infinite-dimensional manifold structure for analytic Lie pseudogroups of infinite type

Details An infinite-dimensional manifold structure for analytic Lie pseudogroups of infinite type An infinite-dimensional manifold structure for analytic Lie pseudogroups of infinite type

2004-02-11

arxiv.org/abs/math/0402182v1

Mathematics

Differential Geometry

To appear in International Mathematics Research Notices, 17 pages

Scientific paper

We construct a infinite-dimensional manifold structure adapted to analytic Lie pseudogroups of infinite type. More precisely, we prove that any isotropy subgroup of an analytic Lie pseudogroup of infinite type is a regular infinite-dimensional Lie group, modelled on a locally convex strict inductive limit of Banach spaces. This is an infinite-dimensional generalization to the case of Lie pseudogroups of the classical second fundamental theorem of Lie.

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