After embedding the objects quasifolds into the category $\{$Diffeology$\}$, we associate a $\boldsymbol{C}^*$-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 $\boldsymbol{C}^*$-algebras with a diffeomorphic class of quasifolds.

中文翻译：

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拟折叠、微分学和非对易几何

将对象准折叠嵌入类别 $\{$Diffeology$\}$ 后，我们将 $\boldsymbol{C}^*$-代数与任何准折叠的每个图集相关联，并展示不同的图集如何给出 Morita 等价的代数。这在微分学和非交换几何之间建立了一座新的桥梁——从今天的无理环面的经典例子开始——它将 $\boldsymbol{C}^*$-代数的 Morita 类与拟折叠的微分同胚类相关联。