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Integration of Singular Foliations via Paths by Villatoro, Joel; Garmendia, Alfonso is a scholarly article available to read on EtoBox.

What is Integration of Singular Foliations via Paths about?

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.

Author

Villatoro, Joel; Garmendia, Alfonso

Published

2019

Language

EN