The holonomy of a singular leaf

Abstract

We introduce the holonomy of a singular leaf L of a singular foliation as a sequence of group morphisms from πn(L) to the πn−1 of the universal Lie ∞-algebroid of the transverse foliation of L. We include these morphisms in a long exact sequence, thus relating them to the holonomy groupoid of Androulidakis and Skandalis and to a similar construction by Brahic and Zhu for Lie algebroids.