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Transactions of the American Mathematical Society

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Presentations of noneffective orbifolds

Authors: Andre Henriques and David S. Metzler
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 2481-2499
MSC (2000): Primary 58H05; Secondary 57S10, 18F99
Published electronically: February 2, 2004
MathSciNet review: 2048526
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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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Additional Information

Andre Henriques
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

David S. Metzler
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611

Keywords: Orbifolds, groupoids, stacks, gerbes, group actions
Received by editor(s): February 12, 2003
Received by editor(s) in revised form: April 29, 2003
Published electronically: February 2, 2004
Article copyright: © Copyright 2004 American Mathematical Society