Journal of Lie Theory EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 13, No. 2, pp. 311--327 (2003)

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Determination of the Topological Structure of an Orbifold by its Groups of Orbifold Diffeomerphisms

Josep E. Bozellino and Victor Brunsden

Joseph E. Borzellino
Department of Mathematics
California Polytechnic State University
San Luis Obispo, CA 93407
Victor Brunsden
Department of Mathematics and Statistics
Penn State Altoona
3000 Ivyside Park
Altoona, PA 16601

Abstract: We show that the topological structure of a compact, locally smooth orbifold is determined by its orbifold diffeomorphism group. Let %\break $\Diff^r_{\OrB}(\orbify{O})$ denote the $C^r$ orbifold diffeomorphisms of an orbifold $\orbify{O}$. Suppose that%\break $\Phi\colon\Diff^r_{\OrB}(\orbify{O}_1) \to \Diff^r_{\OrB}(\orbify{O}_2)$ is a group isomorphism between the the orbifold diffeomorphism groups of two orbifolds $\orbify{O}_1$ and $\orbify{O}_2$. We show that $\Phi$ is induced by a homeomorphism $h\colon X_{\orbify{O}_1} \to X_{\orbify{O}_2}$, where $X_\orbify{O}$ denotes the underlying topological space of $\orbify{O}$. That is, $\Phi(f)=h f h^{-1}$ for all $f\in \Diff^r_{\OrB}(\orbify{O}_1)$. Furthermore, if $r > 0$, then $h$ is a $C^r$ manifold diffeomorphism when restricted to the complement of the singular set of each stratum.

Full text of the article:

Electronic version published on: 26 May 2003. This page was last modified: 14 Aug 2003.

© 2003 Heldermann Verlag
© 2003 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition