Published in Journal of Lie Theory, Volume 13, Issue 2, January 1, 2003, pages 311-327.
We show that the topological structure of a compact, locally smooth orbifold is determined by its orbifold diffeomorphism group. Let DiffrOrb (O) denote the Cr orbifold diffeomorphisms of an orbifold O. Suppose that Φ: DiffrOrb(O1) → DiffrOrb (O2) is a group isomorphism between the the orbifold diffeomorphism groups of two orbifolds O1 and O2. We show that Φ is induced by a homeomorphism h: XO1 → XO2 , where XO denotes the underlying topological space of O. That is, Φ (ƒ) = h ƒh-1 for all ƒ ∈ DiffrOrb(O1). Furthermore, if r > 0, then h is a Cr manifold diffeomorphism when restricted to the complement of the singular set of each stratum.
2003 Journal of Lie Theory.