### 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 - 2003 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Journal of Lie Theory*,

*13*(2), 311-327.

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*Journal of Lie Theory*, vol. 13, no. 2, pp. 311-327.

**Determination of the topological structure of an orbifold by its group of orbifold diffeomorphisms.** / Borzellino, Joseph E.; Brunsden, Victor W.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Determination of the topological structure of an orbifold by its group of orbifold diffeomorphisms

AU - Borzellino, Joseph E.

AU - Brunsden, Victor W.

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0041360162&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041360162&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0041360162

VL - 13

SP - 311

EP - 327

JO - Journal of Lie Theory

JF - Journal of Lie Theory

SN - 0949-5932

IS - 2

ER -