Codimension one minimal foliations and the fundamental groups of leaves

Yokoyama, Tomoo; Tsuboi, Takashi

Codimension one minimal foliations and the fundamental groups of leaves
[Feuilletages minimaux de codimension un et les groupes fondamentaux des feuilles]

Yokoyama, Tomoo ; Tsuboi, Takashi

Annales de l'Institut Fourier, Tome 58 (2008), p. 723-731 / Harvested from Numdam

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Résumé
Abstract

Soit $ℱ$ un feuilletage minimal de codimension un transversalement orientable, transversalement analytique réel sur une variété $M$ paracompacte. On démontre que le feuilletage $ℱ$ est sans holonomie si le groupe fondamental de toute la feuille de $ℱ$ est isomorphe à $Z$ . On démontre aussi que le feuilletage $ℱ$ est sans holonomie si le groupe d’homotopie $π_{2} (M) ≅ 0$ et que le groupe fondamental de toute la feuille de $ℱ$ est isomorphe à $Z^{k}$ ( $k \in Z_{\geq 0}$ ).

Let $ℱ$ be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold $M$ . We show that if the fundamental group of each leaf of $ℱ$ is isomorphic to $Z$ , then $ℱ$ is without holonomy. We also show that if $π_{2} (M) ≅ 0$ and the fundamental group of each leaf of $ℱ$ is isomorphic to $Z^{k}$ ( $k \in Z_{\geq 0}$ ), then $ℱ$ is without holonomy.

Publié le : 2008-01-01

MR 2410388 | Zbl 1148.53017

DOI : https://doi.org/10.5802/aif.2366
Classification: 57R30, 53C12
Mots clés: feuilletages, analytique réel, holonomie, groupes fondamentaux des feulles

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     title = {Codimension one minimal foliations and the fundamental groups of leaves},
     journal = {Annales de l'Institut Fourier},
     volume = {58},
     year = {2008},
     pages = {723-731},
     doi = {10.5802/aif.2366},
     zbl = {1148.53017},
     mrnumber = {2410388},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2008__58_2_723_0}
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Yokoyama, Tomoo; Tsuboi, Takashi. Codimension one minimal foliations and the fundamental groups of leaves. Annales de l'Institut Fourier, Tome 58 (2008) pp. 723-731. doi : 10.5802/aif.2366. http://gdmltest.u-ga.fr/item/AIF_2008__58_2_723_0/

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