On symmetries of singular foliations - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

On symmetries of singular foliations

Ruben Louis
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Résumé

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 Lie ∞-algebroid of F. We deduce from this general result several geometrical consequences. For instance, we give an example of a Lie algebra action on a sub-affine variety which cannot be extended 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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Dates et versions

hal-03738952 , version 1 (26-07-2022)
hal-03738952 , version 2 (20-04-2023)

Identifiants

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Ruben Louis. On symmetries of singular foliations. 2022. ⟨hal-03738952v1⟩
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