Integration of singular subalgebroids by diffeological groupoids

TL;DR

This paper develops a new integration theory for singular subalgebroids using diffeological groupoids, distinguishing between holonomy groupoids and graphs based on their properties.

Contribution

It introduces a novel differentiation-integration framework for singular subalgebroids via a specific class of diffeological groupoids.

Findings

Holonomy groupoids satisfy a submersive property.

Graphs do not satisfy the submersive property.

The framework differentiates between holonomy groupoids and graphs.

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.