Quasifolds, Diffeology And Noncommutative Geometry. Patrick Iglesias-Zemmour & Elisa Prat
11/05/2020
Abstract. After embedding the objects quasifolds into the category Diffeology, we associate a C∗-agebra with every atlas of any quasifold, and show how different atlases give Morita equivalent algebras. This builds a new bridge between diffeology and noncommutative geometry — beginning with the today classical example of the irrational torus — which associates a Morita class of C∗ -algebras with a diffeomorphic class of quasifolds.
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