[Feuilletages transversalement homogènes non unimodulaires]
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 .
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 .
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Keywords: Transversely homogeneous foliation, Lie foliation, base-like cohomology, unimodular foliation
Mot clés : Feuilletage transversalement homogène, feuilletage de Lie, cohomologie basique, feuilletage unimodulaire
@article{AIF_2021__71_2_849_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},
pages = {849--887},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {71},
number = {2},
year = {2021},
doi = {10.5802/aif.3412},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.3412/}
}
TY - JOUR AU - Macías-Virgós, Enrique AU - Martín-Méndez, Pedro L. TI - Non-unimodular transversely homogeneous foliations JO - Annales de l'Institut Fourier PY - 2021 SP - 849 EP - 887 VL - 71 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.3412/ DO - 10.5802/aif.3412 LA - en ID - AIF_2021__71_2_849_0 ER -
%0 Journal Article %A Macías-Virgós, Enrique %A Martín-Méndez, Pedro L. %T Non-unimodular transversely homogeneous foliations %J Annales de l'Institut Fourier %D 2021 %P 849-887 %V 71 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.3412/ %R 10.5802/aif.3412 %G en %F AIF_2021__71_2_849_0
Macías-Virgós, Enrique; Martín-Méndez, Pedro L. Non-unimodular transversely homogeneous foliations. Annales de l'Institut Fourier, Tome 71 (2021) no. 2, pp. 849-887. doi : 10.5802/aif.3412. http://www.numdam.org/articles/10.5802/aif.3412/
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