Codimension one minimal foliations whose leaves have fundamental groups with the same polynomial growth

Tomoo Yokoyama

doi:10.1016/j.crma.2012.03.008

Topology

Codimension one minimal foliations whose leaves have fundamental groups with the same polynomial growth

Presented by: Jean-Pierre Demailly

Tomoo Yokoyama ¹

¹ Creative Research Institution, Hokkaido University, North 21, West 10, Kita-ku, Sapporo 001-0021, Japan

Comptes Rendus. Mathématique, Volume 350 (2012) no. 5-6, pp. 285-287.

Abstract
Résumé

Let $F$ be a transversely orientable codimension one minimal foliation without vanishing cycles of a manifold M and $k \in Z_{⩾ 0}$ . We show that if the fundamental group of each leaf of $F$ has polynomial growth of degree k, then the foliation $F$ is without holonomy.

Soit $F$ une feuilletage minimal de codimension un sur une variété M et $k \in Z_{⩾ 0}$ . Supposons que $F$ nʼa pas de cycles évanouissants. On démontre que le feuilletage $F$ est sans holonomie si le groupe fondamental de toute la feuille de $F$ est à croissance polynomiale de degré k.

Received: 2011-05-10
Accepted: 2012-03-06
Published online: 2012-03-01

DOI: 10.1016/j.crma.2012.03.008

Author's affiliations:

Tomoo Yokoyama ¹

¹ Creative Research Institution, Hokkaido University, North 21, West 10, Kita-ku, Sapporo 001-0021, Japan

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Tomoo Yokoyama. Codimension one minimal foliations whose leaves have fundamental groups with the same polynomial growth. Comptes Rendus. Mathématique, Volume 350 (2012) no. 5-6, pp. 285-287. doi : 10.1016/j.crma.2012.03.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.03.008/

References
Cited by

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[2] M. Gromov Groups of polynomial growth and expanding maps, Inst. Hautes Etudes Sci. Publ. Math., Volume 53 (1981), pp. 53-73

[3] G. Hector; U. Hirsch Introduction to the Geometry of Foliations. Part B. Foliations of Codimension One, Aspects of Mathematics, vol. E3, Friedr. Vieweg & Sohn, Braunschweig, 1983

[4] S.P. Novikov Topology of foliations, Trudy Moskov. Mat. Obshch., Volume 14 (1965), pp. 248-278

[5] T. Yokoyama Codimension one minimal foliations and the higher homotopy groups of leaves, C. R. Acad. Sci. Paris, Ser. I, Volume 347 (2009), pp. 655-658

[6] T. Yokoyama; T. Tsuboi Codimension one foliations and the fundamental groups of leaves, Ann. Inst. Fourier, Volume 58 (2008) no. 2, pp. 723-731

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