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arXiv · 1912.02148

Integration of singular foliations via paths

Joel Villatoro·Alfonso Garmendia
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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.

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Joel Villatoro, Alfonso Garmendia. 2021-06-14. Integration of singular foliations via paths. https://arxiv.org/abs/1912.02148

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