English

Hausdorff Morita Equivalence of singular foliations

Differential Geometry 2019-02-26 v1

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.

Keywords

Cite

@article{arxiv.1803.00896,
  title  = {Hausdorff Morita Equivalence of singular foliations},
  author = {Alfonso Garmendia and Marco Zambon},
  journal= {arXiv preprint arXiv:1803.00896},
  year   = {2019}
}