Codimension one minimal foliations and the fundamental groups of leaves  [ Feuilletages minimaux de codimension un et les groupes fondamentaux des feuilles ]
Annales de l'Institut Fourier, Tome 58 (2008) no. 2, p. 723-731
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 ).
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.
DOI : https://doi.org/10.5802/aif.2366
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},
     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, Tome 58 (2008) no. 2, pp. 723-731. doi : 10.5802/aif.2366. http://www.numdam.org/item/AIF_2008__58_2_723_0/

[1] Cantwell, John; Conlon, Lawrence Leaf prescriptions for closed 3-manifolds, Trans. Amer. Math. Soc., Tome 236 (1978), pp. 239-261 | MR 645738 | Zbl 0398.57009

[2] Cantwell, John; Conlon, Lawrence 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 1882772 | Zbl 1011.57009

[3] Epstein, D. B. A.; Millett, K. C.; Tischler, D. Leaves without holonomy, J. London Math. Soc. (2), Tome 16 (1977) no. 3, pp. 548-552 | Article | MR 464259 | Zbl 0381.57007

[4] Farrell, F. T.; Jones, L. E. The surgery L-groups of poly-(finite or cyclic) groups, Invent. Math., Tome 91 (1988) no. 3, pp. 559-586 | Article | MR 928498 | Zbl 0657.57015

[5] Haefliger, André Structures feuilletées et cohomologie à valeur dans un faisceau de groupoïdes, Comment. Math. Helv., Tome 32 (1958), pp. 248-329 | Article | MR 100269 | Zbl 0085.17303

[6] Hirsch, M. A stable analytic foliation with only exceptional minimal sets, Dynamical Systems, Springer, Berlin, Heidelberg, New York (Lecture Notes in Math.) Tome 468 (1975), p. 9-10 | Zbl 0309.53053

[7] Kerékjártó, B. Vorlesungen uber Topologie, Springer, Berlin Tome I (1923)

[8] Novikov, S. P. Topology of foliations, Trans. Mosc. Math. Soc., Tome 14 (1965), pp. 268-304 (translation from Tr. Mosk. Mat. Obshch. 14, 248-278 (1965)) | MR 200938 | Zbl 0247.57006

[9] Richards, I. On the classification of noncompact surfaces, Trans. Amer. Math. Soc., Tome 106 (1963), pp. 259-269 | Article | MR 143186 | Zbl 0156.22203

[10] Tischler, D. On fibering certain foliated manifolds over S 1 , Topology, Tome 9 (1970), p. 153-154 | Article | MR 256413 | Zbl 0177.52103