On symmetries of singular foliations
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.
Domaines
Géométrie différentielle [math.DG]Origine | Fichiers produits par l'(les) auteur(s) |
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