Codimension one minimal foliations and the fundamental groups of leaves
Annales de l'Institut Fourier, Volume 58 (2008) no. 2, pp. 723-731.

Let 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 is isomorphic to Z, then is without holonomy. We also show that if π 2 (M)0 and the fundamental group of each leaf of is isomorphic to Z k (kZ 0 ), then is without holonomy.

Soit un feuilletage minimal de codimension un transversalement orientable, transversalement analytique réel sur une variété M paracompacte. On démontre que le feuilletage est sans holonomie si le groupe fondamental de toute la feuille de est isomorphe à Z. On démontre aussi que le feuilletage est sans holonomie si le groupe d’homotopie π 2 (M)0 et que le groupe fondamental de toute la feuille de est isomorphe à Z k (kZ 0 ).

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

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)
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.2366/

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