Quotients of singular foliations and Lie 2-group actions

2019/04/18 by Garmendia, Alfonso, Zambon, Marco
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.08890

Abstract

Every singular foliation has an associated topological groupoid, called holonomy groupoid (see arXiv:math/0612370). In this note we exhibit some functorial properties of this assignment: if a foliated manifold (M,F_M) is the quotient of a foliated manifold (P,F_P) 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 analog statement holds under suitable assumptions, yielding a Lie 2-group action on the holonomy groupoid.

Related

• Groupoids and singular foliations
• The holonomy Lie ∞-groupoid of a singular foliation I
• Integration of singular foliations via paths
• The holonomy of a singular leaf
• Holonomy and monodromy groupoids