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.
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 ().
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
@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{\textquoteright}institut Fourier}, volume = {58}, number = {2}, year = {2008}, doi = {10.5802/aif.2366}, mrnumber = {2410388}, zbl = {1148.53017}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2366/} }
TY - JOUR AU - Yokoyama, Tomoo AU - Tsuboi, Takashi TI - Codimension one minimal foliations and the fundamental groups of leaves JO - Annales de l'Institut Fourier PY - 2008 SP - 723 EP - 731 VL - 58 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2366/ DO - 10.5802/aif.2366 LA - en ID - AIF_2008__58_2_723_0 ER -
%0 Journal Article %A Yokoyama, Tomoo %A Tsuboi, Takashi %T Codimension one minimal foliations and the fundamental groups of leaves %J Annales de l'Institut Fourier %D 2008 %P 723-731 %V 58 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2366/ %R 10.5802/aif.2366 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.2366/
[1] Leaf prescriptions for closed -manifolds, Trans. Amer. Math. Soc., Volume 236 (1978), pp. 239-261 | MR | Zbl
[2] Endsets of exceptional leaves; a theorem of G. Duminy, Foliations: geometry and dynamics (Warsaw, 2000), World Sci. Publ., River Edge, NJ, 2002, pp. 225-261 | MR | Zbl
[3] Leaves without holonomy, J. London Math. Soc. (2), Volume 16 (1977) no. 3, pp. 548-552 | DOI | MR | Zbl
[4] The surgery -groups of poly-(finite or cyclic) groups, Invent. Math., Volume 91 (1988) no. 3, pp. 559-586 | DOI | MR | Zbl
[5] Structures feuilletées et cohomologie à valeur dans un faisceau de groupoïdes, Comment. Math. Helv., Volume 32 (1958), pp. 248-329 | DOI | MR | Zbl
[6] A stable analytic foliation with only exceptional minimal sets, Dynamical Systems (Lecture Notes in Math.), Volume 468, Springer, Berlin, Heidelberg, New York, 1975, pp. 9-10 | Zbl
[7] Vorlesungen uber Topologie, I, Springer, Berlin, 1923
[8] Topology of foliations, Trans. Mosc. Math. Soc., Volume 14 (1965), pp. 268-304 translation from Tr. Mosk. Mat. Obshch. 14, 248-278 (1965) | MR | Zbl
[9] On the classification of noncompact surfaces, Trans. Amer. Math. Soc., Volume 106 (1963), pp. 259-269 | DOI | MR | Zbl
[10] On fibering certain foliated manifolds over , Topology, Volume 9 (1970), pp. 153-154 | DOI | MR | Zbl
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