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A manifold structure for the group of orbifold diffeomorphisms

Joseph E. Borzellino

Abstract

A well-known result in the theory of differentiable dynamical systems states that the set of smooth maps between a compact manifold M and a manifold N has the structure of a smooth infinite-dimensional manifold. By considering only diffeomorphisms, one sees that Diff(M) is an infinite-dimensional group with a local manifold structure. In this talk, I will discuss generalizations of this result to the group of orbifold diffeomorphisms. Time permitting, I will discuss some recent work on analogous results for other classes of smooth orbifold maps between orbifolds. Part of the talk will review orbifolds and the mappings between them. This is joint work with V. Brunsden of Penn State Altoona.

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