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Quotients of singular foliations and Lie 2-group actions.
- Source :
- Journal of Noncommutative Geometry; 2021, Vol. 15 Issue 4, p1251-1283, 33p
- Publication Year :
- 2021
-
Abstract
- 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, F<subscript>M</subscript>) is the quotient of a foliated manifold (P, F<subscript>P</subscript>) 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16616952
- Volume :
- 15
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Journal of Noncommutative Geometry
- Publication Type :
- Academic Journal
- Accession number :
- 157089471
- Full Text :
- https://doi.org/10.4171/JNCG/434