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Quasifolds, Diffeology and Noncommutative Geometry (2005.09283v2)

Published 19 May 2020 in math.DG

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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