The diffeomorphism group of a non-compact orbifold

Abstract

We endow the diffeomorphism group of a paracompact (reduced) orbifold with the structure of an infinite dimensional Lie group modelled on the space of compactly supported sections of the tangent orbibundle. For a second countable orbifold, we prove that this Lie group is C^0-regular and thus regular in the sense of Milnor. Furthermore an explicit characterization of the Lie algebra associated to the diffeomorphism group of an orbifold is given.

184 pp, LaTex and TikZ. V4: updated some remarks and literature, corrected typos and minor errors. The results remain unchanged. For the reader's convenience, the appendix contains some definitions and known facts from A. Pohl's preprint arXiv:1001.0668 and H. Glockner's preprint arXiv:math/0408008 which are used in the text

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• Differentiable mappings on products with different degrees of differentiability in the two factors
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• The diffeomorphism group of a non-compact orbifold
• Implicit functions from topological vector spaces to Fréchet spaces in the presence of metric estimates

Cited by in corpus (11)

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• Lie groupoids of mappings taking values in a Lie groupoid
• The groupoid structure of groupoid morphisms
• Extending Whitney's extension theorem: nonlinear function spaces
• The smooth Hom-stack of an orbifold
• Lie Theory for Asymptotic Symmetries in General Relativity: The NU Group
• Introduction to orbifolds
• A Lie group structure on the group of real analytic diffeomorphisms of a compact real analytic manifold with corners