TY  - JOUR
A1  - Garmendia, Alfonso
A1  - Zambon, Marco
T1  - Quotients of singular foliations and Lie 2-group actions
T2  - Journal of noncommutative geometry
N2  - Androulidakis-Skandalis (2009) showed that every singular foliation has an associated topological groupoid, called holonomy groupoid. In this note, we exhibit some functorial properties of this assignment: if a foliated manifold (M, FM ) is the quotient of a foliated manifold (P, FP ) along a surjective submersion with connected fibers, then the same is true for the corresponding holonomy groupoids. For quotients by a Lie group action, an analogue statement holds under suitable assumptions, yielding a Lie 2-group action on the holonomy groupoid.
KW  - Lie groupoid
KW  - singular foliation
KW  - fibration
Y1  - 2021
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/61128
SN  - 1661-6952
SN  - 1661-6960
VL  - 15
IS  - 4
SP  - 1251
EP  - 1283
PB  - EMS Press, an imprint of the European Mathematical Society - EMS - Publishing House GmbH, Institut für Mathematik, Technische Universität Berlin
CY  - Berlin
ER  -