The holonomy of a singular leaf

Camille Laurent-Gengoux (1) , Leonid Ryvkin (2, 3, 4)

1 IECL - Institut Élie Cartan de Lorraine
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
3 Georg-August-University = Georg-August-Universität Göttingen
4 Universität Duisburg-Essen [Essen]

We introduce the holonomy of a singular leaf L of a singular foliation as a sequence of group morphisms from π_n(L) to the π_n−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.

Domains: Mathematics [math]; Differential Geometry [math.DG]

Camille Laurent-Gengoux, Leonid Ryvkin. The holonomy of a singular leaf. Selecta Mathematica (New Series), 2022, 28 (2), pp.45. ⟨10.1007/s00029-021-00753-z⟩. ⟨hal-03669113⟩