Integration of singular subalgebroids by diffeological groupoids

Abstract

We establish an integration theory for singular subalgebroids, by diffeological groupoids. To do so, we single out a class of diffeological groupoids satisfying specific properties, and we introduce a differentiation-integration procedure under which they correspond to singular subalgebroids. Our definition of integration distinguishes the holonomy groupoid from the graph, although both differentiate to the original singular subalgebroid: the holonomy groupoid satisfies a certain submersive property, while the graph does not.