Title
Determination of the Topological Structure of an Orbifold by its Group of Orbifold Diffeomerphisms
Recommended Citation
Published in Journal of Lie Theory, Volume 13, Issue 2, January 1, 2003, pages 311-327.
Abstract
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.
Disciplines
Mathematics
Copyright
2003 Journal of Lie Theory.
Included in
URL: https://digitalcommons.calpoly.edu/math_fac/107