Codimension one minimal foliations and the fundamental groups of leaves

Yokoyama, Tomoo; Tsuboi, Takashi

doi:10.5802/aif.2366

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

Yokoyama, Tomoo ¹ ; Tsuboi, Takashi ²

¹ The University of Tokyo Graduate School of Mathematical Sciences Komaba Meguro, Tokyo 153-8914, Japan
² The University of Tokyo Graduate School of Mathematical Sciences Komaba Meguro, Tokyo 153-8914 (Japan)

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

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.

MR Zbl

DOI : 10.5802/aif.2366

Classification : 57R30, 53C12
Keywords: Foliations, real-analytic, holonomy, fundamental groups of leaves
Mot clés : feuilletages, analytique réel, holonomie, groupes fondamentaux des feulles

Affiliations des auteurs :

Yokoyama, Tomoo ¹ ; Tsuboi, Takashi ²

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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) no. 2, pp. 723-731. doi : 10.5802/aif.2366. http://www.numdam.org/articles/10.5802/aif.2366/

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