The holonomy of a singular leaf (Q832407)

\textit{I. Androulidakis} and \textit{G. Skandalis} [J. Reine Angew. Math. 626, 1--37 (2009; Zbl 1161.53020)] gave a construction for the holonomy groupoid of any singular foliation. Androulidakis and Zambon formulated a holonomy map for singular foliations, which is defined on the holonomy groupoid, rather than the fundamental group of a leaf, as it happens with regular foliations. On the other hand, Laurent-Gengoux, Lavau and Strobl established a universal Lie-\(\infty\) algebroid to every singular foliation. In the paper under review, the authors construct higher holonomy maps, defined on \(\pi_n(L)\), where \(L\) is a singular leaf \(L\). They take values in the \((n-1)\)-th homotopy group of the universal Lie-\(\infty\) algebroid associated with the transversal foliation to \(L\). Moreover, they show that these holonomy maps form a long exact sequence.