Quasifolds, Diffeology and Noncommutative Geometry

TL;DR

This paper establishes a connection between quasifolds, diffeology, and noncommutative geometry by associating C*-algebras to quasifolds and demonstrating Morita equivalence across different atlases, bridging these mathematical areas.

Contribution

It introduces a method to embed quasifolds into diffeology and associates Morita equivalent C*-algebras to different atlases, linking diffeology with noncommutative geometry.

Findings

Associates C*-algebras to quasifolds via atlases

Shows Morita equivalence of algebras from different atlases

Bridges diffeology and noncommutative geometry through Morita classes

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.