Hausdorff Morita equivalence of singular foliations

© 2018, Springer Nature B.V. We introduce a notion of equivalence for singular foliations—understood as suitable families of vector fields—that preserves their transverse geometry. Associated with 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 1980s.

Publication year:2019

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Authors from:Higher Education

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