After embedding the objects quasifolds into the category Diffeology, we associate a -algebra 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 -algebras with a diffeomorphic class of quasifolds.
Cite this article
Patrick Iglesias-Zemmour, Elisa Prato, Quasifolds, diffeology and noncommutative geometry. J. Noncommut. Geom. 15 (2021), no. 2, pp. 735–759DOI 10.4171/JNCG/419