Codimension one minimal foliations and the higher homotopy groups of leaves

Tomoo Yokoyama

doi:10.1016/j.crma.2009.03.017

Topology

Codimension one minimal foliations and the higher homotopy groups of leaves

Presented by: Étienne Ghys

Tomoo Yokoyama ¹

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

Abstract (Original language)
Résumé

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 $\tilde{F}$ 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: 2007-04-23
Accepted: 2009-03-23
Published online: 2009-04-11

DOI: 10.1016/j.crma.2009.03.017

Author's affiliations:

Tomoo Yokoyama ¹

¹ Graduate School of Mathematical Sciences, University of Tokyo, Komaba Meguro, Tokyo 153-8914, Japan

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Tomoo Yokoyama. 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

References
Cited by

[1] C. Lamoureux 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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