The holonomy of a singular leaf

Laurent-Gengoux, Camille; Ryvkin, Leonid

doi:10.1007/s00029-021-00753-z

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2022

2023

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Cited by 2 publications

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“…Example 1.9. The following example is taken from [16], and follows the same patterns as in Examples 1.7 and 1.8. Let (M, F) be a singular foliation on a manifold M and L ⊂ M a leaf.…”

Section: Introductionmentioning

confidence: 99%

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On symmetries of singular foliations

Louis¹

2022

Preprint

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This paper shows that a weak symmetry action of a Lie algebra g on a singular foliation F induces a unique (up to homotopy) Lie ∞-morphism from g to the DGLA of vector fields on a universal N Q-manifold over F. We deduce from this general result several geometric consequences. For instance, we give an example of a weak action of Lie algebra, i.e., an action on the leaf space which cannot be turned into an action on the ambient space. Last, we introduce the notion of tower of bi-submersions over a singular foliations and lift symmetries to those.

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“…Example 1.9. The following example is taken from [16], and follows the same patterns as in Examples 1.7 and 1.8. Let (M, F) be a singular foliation on a manifold M and L ⊂ M a leaf.…”

Section: Introductionmentioning

confidence: 99%

“…Let (M, F) be a singular foliation on a manifold M and L ⊂ M a leaf. Let [L, M ] be a neighbourhood of L in M equipped with some projection π : M −→ L. According to [16], upon replacing [L, M ] be a smaller neighborhood of L if necessary, there exists an Ehresmann connection (that is a vector sub-bundle…”

Section: Introductionmentioning

confidence: 99%