We show that the topological structure of a compact, locally smooth orbifold is determined by its orbifold diffeomorphism group. Let Diff Orbr(O) denote the Cr orbifold diffeomorphisms of an orbifold O. Suppose that Φ: DiffOrbr(O 1) → DiffOrbr(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(f) = hfh -1 for all f ∈ DiffOrbr(O1). Furthermore, if r > 0, then h is a Cr manifold diffeomorphism when restricted to the complement of the singular set of each stratum.
|Original language||English (US)|
|Number of pages||17|
|Journal||Journal of Lie Theory|
|State||Published - Jan 1 2003|
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory