Codimension one minimal foliations and the fundamental groups of leaves

Yokoyama, Tomoo; Tsuboi, Takashi

doi:10.5802/aif.2366

Yokoyama, Tomoo; Tsuboi, Takashi

Annales de l'Institut Fourier, Volume 58 (2008) no. 2, p. 723-731

Abstract
Résumé

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.

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 $Z^{k}$ ( $k \in Z_{\geq 0}$ ).

MR 2410388 | Zbl 1148.53017

DOI : https://doi.org/10.5802/aif.2366
Classification: 57R30, 53C12
Keywords: Foliations, real-analytic, holonomy, fundamental groups of leaves

@article{AIF_2008__58_2_723_0,
     author = {Yokoyama, Tomoo and Tsuboi, Takashi},
     title = {Codimension one minimal foliations and the fundamental groups of leaves},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {58},
     number = {2},
     year = {2008},
     pages = {723-731},
     doi = {10.5802/aif.2366},
     mrnumber = {2410388},
     zbl = {1148.53017},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2008__58_2_723_0}
}

Yokoyama, Tomoo; Tsuboi, Takashi. Codimension one minimal foliations and the fundamental groups of leaves. Annales de l'Institut Fourier, Volume 58 (2008) no. 2, pp. 723-731. doi : 10.5802/aif.2366. http://www.numdam.org/item/AIF_2008__58_2_723_0/

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