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arXiv · 1803.00896

Hausdorff Morita Equivalence of singular foliations

Alfonso Garmendia·Marco Zambon
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Abstract

We introduce a notion of equivalence for singular foliations - understood as suitable families of vector fields - that preserves their transverse geometry. Associated to every singular foliation there is a holonomy groupoid, by the work of Androulidakis-Skandalis. We show that our notion of equivalence is compatible with this assignment, and as a consequence we obtain several invariants. Further, we show that it unifies some of the notions of transverse equivalence for regular foliations that appeared in the 1980's.

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BibTeXRIS

Alfonso Garmendia, Marco Zambon. 2018-03-02. Hausdorff Morita Equivalence of singular foliations. https://arxiv.org/abs/1803.00896

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