The diffeomorphism group of a non-compact orbifold

TL;DR

This paper constructs an infinite-dimensional Lie group structure on the diffeomorphism group of a non-compact orbifold, proving its regularity and characterizing its Lie algebra.

Contribution

It introduces a Lie group structure on the diffeomorphism group of a non-compact orbifold and provides an explicit Lie algebra characterization.

Findings

The diffeomorphism group forms a C^0-regular Lie group.

The Lie algebra of the diffeomorphism group is explicitly characterized.

The construction applies to paracompact, reduced orbifolds.

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.