Determination of the Topological Structure of an Orbifold by its Group of Orbifold Diffeomorphisms

We show that the topological structure of a compact, locally smooth orbifold is determined by its orbifold diffeomorphism group.Let Diff r Orb (O) denote the C r orbifold diffeomorphisms of an orbifold O .Suppose that : Diff) is a group isomorphism between the the orbifold diffeomorphism groups of two orbifolds O 1 and O 2 .We show that is induced by a homeomorphism h : X O1 X O2 , where X O denotes the underlying topological space of O .That is, (f ) = hf h -1 for all f Diff r Orb (O 1 ) .Furthermore, if r > 0, then h is a C r manifold diffeomorphism when restricted to the complement of the singular set of each stratum.* We would like to thank A. Banyaga for helpful conversations leading to improvements of the original manuscript.