Soit un feuilletage minimal de codimension un transversalement orientable, transversalement analytique réel sur une variété paracompacte. On démontre que le feuilletage est sans holonomie si le groupe fondamental de toute la feuille de est isomorphe à . On démontre aussi que le feuilletage est sans holonomie si le groupe d’homotopie et que le groupe fondamental de toute la feuille de est isomorphe à ().
Let be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold . We show that if the fundamental group of each leaf of is isomorphic to , then is without holonomy. We also show that if and the fundamental group of each leaf of is isomorphic to (), then is without holonomy.
Classification : 57R30, 53C12
Mots clés : feuilletages, analytique réel, holonomie, groupes fondamentaux des feulles
@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}, pages = {723--731}, publisher = {Association des Annales de l'institut Fourier}, volume = {58}, number = {2}, year = {2008}, doi = {10.5802/aif.2366}, mrnumber = {2410388}, zbl = {1148.53017}, language = {en}, url = {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, Tome 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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