## Abstract

We show that the topological structure of a compact, locally smooth orbifold is determined by its orbifold diffeomorphism group. Let Diff _{Orb}^{r}(O) denote the C^{r} orbifold diffeomorphisms of an orbifold O. Suppose that Φ: Diff_{Orb}^{r}(O _{1}) → Diff_{Orb}^{r}(O_{2}) is a group isomorphism between the the orbifold diffeomorphism groups of two orbifolds O_{1} and O_{2}. We show that Φ is induced by a homeomorphism h: X_{O1} → X_{O2}, where X_{O} denotes the underlying topological space of O. That is, Φ(f) = hfh ^{-1} for all f ∈ Diff_{Orb}^{r}(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.

Original language | English (US) |
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Pages (from-to) | 311-327 |

Number of pages | 17 |

Journal | Journal of Lie Theory |

Volume | 13 |

Issue number | 2 |

State | Published - Jan 1 2003 |

## All Science Journal Classification (ASJC) codes

- Algebra and Number Theory