The diffeomorphism group of a non-compact orbifold
Volume 507 / 2015
Dissertationes Mathematicae 507 (2015), 1-179
MSC: Primary 58D05; Secondary 22E65, 46T05, 57R18, 53C20, 58D25.
DOI: 10.4064/dm507-0-1
Abstract
We endow the diffeomorphism group ${\rm Diff}_{\rm Orb}(Q,\mathcal U)$ of a paracompact (reduced) orbifold with the structure of an infinite-dimensional Lie group modeled on the space of compactly supported sections of the tangent orbibundle. For a second countable orbifold, we prove that ${\rm Diff}_{\rm Orb}(Q,\mathcal U)$ is $C^0$-regular, and thus regular in the sense of Milnor. Furthermore, an explicit characterization of the Lie algebra associated to ${\rm Diff}_{\rm Orb}(Q,\mathcal U)$ is given.
