# Topologie locale des espaces de feuilletages des variétés fermées de dimension 3

Abstract : We are interested in orientable foliations by surfaces on compact orientable three-manifolds without boundary. We prove that two such foliations on a closed orientable three-manifold are homotopic if they are taut and sufficiently close. First of all, we prove a version with parameter'' of a theorem of Thurston according to which foliations of the torus can be extended to foliations of the solid torus. In this work we construct such an extension and we use Herman's theorem on conjugacy of circle diffeomorphisms to rotations to ensure that this extension is continuous with respect to the foliations. Then we prove that the space of foliations transverse to a fiber bundle over a closed orientable surface is homotopic to a point. Finally, we establish the announced result by means of an idea of Thurston and the previous results. We deduce consequences on the local topology of foliations by surfaces on closed three-manifolds.
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https://tel.archives-ouvertes.fr/tel-00008258
Contributor : Audrey Larcanché <>
Submitted on : Wednesday, January 26, 2005 - 11:14:07 AM
Last modification on : Sunday, November 29, 2020 - 3:24:11 AM
Long-term archiving on: : Friday, April 2, 2010 - 9:10:59 PM

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• HAL Id : tel-00008258, version 1

### Citation

Audrey Larcanché. Topologie locale des espaces de feuilletages des variétés fermées de dimension 3. Mathématiques [math]. Université des Sciences et Technologie de Lille - Lille I, 2004. Français. ⟨tel-00008258⟩

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