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, pp. 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 : 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)
@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},
     zbl = {1148.53017},
     mrnumber = {2410388},
     language = {en},
     url = {http://archive.numdam.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  - http://archive.numdam.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 http://archive.numdam.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, Tome 58 (2008) no. 2, pp. 723-731. doi : 10.5802/aif.2366. http://archive.numdam.org/articles/10.5802/aif.2366/

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

[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 | Zbl

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

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

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

[6] Hirsch, M. 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] Kerékjártó, B. Vorlesungen uber Topologie, I, Springer, Berlin, 1923

[8] Novikov, S. P. 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] Richards, I. On the classification of noncompact surfaces, Trans. Amer. Math. Soc., Volume 106 (1963), pp. 259-269 | DOI | MR | Zbl

[10] Tischler, D. On fibering certain foliated manifolds over S 1 , Topology, Volume 9 (1970), pp. 153-154 | DOI | MR | Zbl

Cité par Sources :