no. 11-12
Topology
Codimension one minimal foliations and the higher homotopy groups of leaves

Presented by: Étienne Ghys

Yokoyama, Tomoo1
1 Graduate School of Mathematical Sciences, University of Tokyo, Komaba Meguro, Tokyo 153-8914, Japan
Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 655-658.

Let F be a codimension one foliation of an aspherical manifold M. Assume that F has no vanishing cycles. If there is an aspherical dense leaf of F, then each leaf of F is aspherical. If F is minimal and the universal covering of a leaf of F is not k-connected, then the universal coverings of no leaves are k-connected.

Soit F une feuilletage de codimension un sur une variété M asphérique. Supposons que F n'a pas de cycles évanouissants. S'il y a une feuille asphérique et dense, alors toute feuille de F est asphérique. Si F˜ est minimal et le revêtement universel d'une feuille n'est pas k-connexe, alors le revêtement universel d'aucune feuille est k-connexe.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.03.017
Yokoyama, Tomoo 1

1 Graduate School of Mathematical Sciences, University of Tokyo, Komaba Meguro, Tokyo 153-8914, Japan 
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Yokoyama, Tomoo. Codimension one minimal foliations and the higher homotopy groups of leaves. Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 655-658. doi : 10.1016/j.crma.2009.03.017. http://www.numdam.org/articles/10.1016/j.crma.2009.03.017/

[1] Lamoureux, C. Groupes d'homologie et d'homotopie d'ordre supérieur des variétés compactes ou non compactes feuilletées en codimension 1, C. R. Acad. Sci. Paris, Ser. A–B, Volume 280 (1975) no. 7 (Ai, A411–A414)

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