Integration of singular foliations via paths
Abstract
We give a new construction of the holonomy and fundamental groupoids of a singular foliation. In contrast with the existing construction of Androulidakis and Skandalis, our method proceeds by taking a quotient of an infinite dimensional space of paths. This strategy is a direct extension of the classical construction for regular foliations and mirrors the integration of Lie algebroids via paths (per Crainic and Fernandes). In this way, we obtain a characterization of the holonomy and fundamental groupoids of a singular foliation that more clearly reflects the homotopic character of these invariants. As an application of our work, we prove that the constructions of the fundamental and holonomy groupoid of a foliation have functorial properties.
Cite
@article{arxiv.1912.02148,
title = {Integration of singular foliations via paths},
author = {Joel Villatoro and Alfonso Garmendia},
journal= {arXiv preprint arXiv:1912.02148},
year = {2021}
}