Journal of Lie Theory Vol. 13, No. 2, pp. 311327 (2003) 

Determination of the Topological Structure of an Orbifold by its Groups of Orbifold DiffeomerphismsJosep E. Bozellino and Victor BrunsdenJoseph E. BorzellinoDepartment of Mathematics California Polytechnic State University San Luis Obispo, CA 93407 jborzell@calpoly.edu and Victor Brunsden Department of Mathematics and Statistics Penn State Altoona 3000 Ivyside Park Altoona, PA 16601 vwb2@psu.edu 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
