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arxiv: 1803.00896 · v1 · submitted 2018-03-02 · 🧮 math.DG

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Hausdorff Morita Equivalence of singular foliations

Alfonso Garmendia , Marco Zambon
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classification 🧮 math.DG
keywords equivalencefoliationssingularnotiontransverseandroulidakis-skandalisappearedassignment
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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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