Integration of Singular Foliations via Paths

Author:

Garmendia Alfonso1,Villatoro Joel2

Affiliation:

1. KU Leuven Departement Wiskunde, Celestijnenlaan 200B, 3001 Leuven, Belgium

2. Institut für Mathematik, Haus 9, Karl-Liebknecht-Strae 24, 14476 Potsdam, Germany

Abstract

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.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Reference26 articles.

1. The holonomy groupoid of a singular foliation;Androulidakis;Reine Angew. Math.,2009

2. Smoothness of holonomy covers for singular foliations and essential isotropy;Androulidakis;Math. Z.,2013

3. Holonomy transformations for singular foliations;Androulidakis;Adv. Math.,2014

4. Tangent spaces and tangent bundles for diffeological spaces;Christensen;Cah. Topol. Géom. Différ. Catég,2016

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