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Journal of Lie Theory 18 (2008), No. 4, 979--1007
Copyright Heldermann Verlag 2008

A Manifold Structure for the Group of Orbifold Diffeomorphisms of a Smooth Orbifold

Joseph E. Borzellino
Dept. of Mathematics, California Polytechnic State University, 1 Grand Avenue, San Luis Obispo, CA 93407, U.S.A.

Victor Brunsden
Dept. of Mathematics and Statistics, Penn State Altoona, 3000 Ivyside Park, Altoona, PA 16601, U.S.A.


For a compact, smooth $C^r$ orbifold (without boundary), we show that the topological structure of the orbifold diffeomorphism group is a Banach manifold for $1\le r<\infty$ and a Fr\'echet manifold if $r=\infty$. In each case, the local model is the separable Banach (Fr\'echet) space of $C^r$, respectively, $C^\infty$ orbisections of the tangent orbibundle.

Keywords: Orbifolds, diffeomorphism groups, topological transformation groups, homeomorphism groups.

MSC: 57S05, 22F50, 54H99; 22E65

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