Non-unimodular transversely homogeneous foliations
[Feuilletages transversalement homogènes non unimodulaires]
Annales de l'Institut Fourier, Online first, 39 p.

En calculant sa cohomologie basique, on donne des conditions suffisantes pour qu’un feuilletage transversalement homogène defini sur une variété compacte soit minimalisable. Comme application, on démontre que si le feuilletage est non unimodulaire alors soit la variété ambiante, soit l’adhérence des feuilles, soit un fibré principal associé au feuilletage, fibrent sur S 1 .

We give sufficient conditions for the tautness of a transversely homogenous foliation defined on a compact manifold, by computing its base-like cohomology. As an application, we prove that if the foliation is non-unimodular then either the ambient manifold, the closure of the leaves or the total space of an associated principal bundle fiber over S 1 .

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DOI : https://doi.org/10.5802/aif.3412
Classification : 57R30,  53C12
Mots clés : Feuilletage transversalement homogène, feuilletage de Lie, cohomologie basique, feuilletage unimodulaire
@unpublished{AIF_0__0_0_A12_0,
     author = {Mac{\'\i}as-Virg\'os, Enrique and Mart{\'\i}n-M\'endez, Pedro L.},
     title = {Non-unimodular transversely homogeneous foliations},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     year = {2021},
     doi = {10.5802/aif.3412},
     language = {en},
     note = {Online first},
}
Macías-Virgós, Enrique; Martín-Méndez, Pedro L. Non-unimodular transversely homogeneous foliations. Annales de l'Institut Fourier, Online first, 39 p.

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