Noncommutative geometry and diffeology: The case of orbifolds

Abstract

We establish a first structural link between noncommutative geometry and diffeology, in the particular case of orbifolds. Precisely, we associate a structure groupoid with every atlas of a diffeological orbifold. We show that different atlases give equivalent groupoids, that generates strongly Morita equivalent ${\mathbf{C}}^{\ast }$-algebras, according to standards. Thus, diffeomorphisms translate naturally into Morita equivalences.