Presentations of noneffective orbifolds

Henriques, Andre; Metzler, David

doi:10.1090/S0002-9947-04-03379-3

Presentations of noneffective orbifolds
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by Andre Henriques and David S. Metzler PDF

Trans. Amer. Math. Soc. 356 (2004), 2481-2499 Request permission

Abstract:

It is well known that an effective orbifold $M$ (one for which the local stabilizer groups act effectively) can be presented as a quotient of a smooth manifold $P$ by a locally free action of a compact Lie group $K$. We use the language of groupoids to provide a partial answer to the question of whether a noneffective orbifold can be so presented. We also note some connections to stacks and gerbes.

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