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arXiv · 1904.08890

Quotients of singular foliations and Lie 2-group actions

Alfonso Garmendia·Marco Zambon
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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 $(M,\mathcal{F}_M)$ is the quotient of a foliated manifold $(P,\mathcal{F}_P)$ 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.

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Alfonso Garmendia, Marco Zambon. 2019-04-18. Quotients of singular foliations and Lie 2-group actions. https://arxiv.org/abs/1904.08890

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