Actions of 2-groupoids on C*-algebras

群胚描述了具有奇点的几何空间，是非交换几何的中心研究对象。几何和数学物理中的几个问题会导致群胚不适用的奇点，一个典型的例子是具有非豪斯多夫完整群胚的叶理。但这些情况可以在高级范畴理论的框架下用2-群胚来描述。这个项目的目标是将C*-代数附加到这样的2-广群上;研究它们在C*-代数上的作用和这种作用的交叉积，以及由此产生的C*-代数的K-理论。2-群胚作用的自然概念比通常的概念更灵活，并且包括绿色的扭曲群作用作为特例。此外，它允许在叶子的完整2-广群的C*-代数上的适当作用，即使完整广群是非Hausdorff的。

Groupoids describe geometric spaces with singularities and are a central object of study in noncommutative geometry. Several problems in geometry and mathematical physics lead to singularities for which groupoids are inadequate; a typical example are foliations with non-Hausdorff holonomy groupoid. But these situations may be described in the framework of higher category theory using 2-groupoids. The goals of this project are to attach C*-algebras to such 2-groupoids; to study their actions on C*-algebras and crossed products for such actions, and the K-theory of the resulting C*-algebras. The natural notion of action for 2-groupoids is more flexible than the usual one and includes Green’s twisted group actions as a special case. Furthermore, it allows for proper actions on C*-algebras of holonomy 2-groupoids of foliations even if the holonomy groupoid is non-Hausdorff.