Integration of singular subalgebroids by diffeological groupoids

2020/08/18 by Iakovos Androulidakis, Marco Zambon, Androulidakis, Iakovos +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · doi:10.48550/arxiv.2008.07976

openalex publication_date 2020/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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