# NIL-ANOSOV ACTIONS

Abstract : We consider Anosov actions of a Lie group $G$ of dimension $k$ on a closed manifold of dimension $k+n.$ We introduce the notion of Nil-Anosov action of $G$ (which includes the case where $G$ is nilpotent) and establishes the invariance by the entire group $G$ of the associated stable and unstable foliations. We then prove a spectral decomposition Theorem for such an action when the group $G$ is nilpotent. Finally, we focus on the case where $G$ is nilpotent and the unstable bundle has codimension one. We prove that in this case the action is a Nil-extension over an Anosov action of an abelian Lie group. In particular: i) if $n \geq 3,$ then the action is topologically transitive, ii) if $n=2,$ then the action is a Nil-extension over an Anosov flow.
Keywords :
Type de document :
Pré-publication, Document de travail
This version contains a serious error which will will be corrected in the published version. 2015

https://hal-univ-avignon.archives-ouvertes.fr/hal-01197491
Contributeur : Thierry Barbot <>
Soumis le : dimanche 5 juin 2016 - 09:47:50
Dernière modification le : dimanche 17 décembre 2017 - 06:54:05
Document(s) archivé(s) le : mardi 6 septembre 2016 - 10:12:15

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Nilp_transitive.pdf
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### Identifiants

• HAL Id : hal-01197491, version 2
• ARXIV : 1509.03816

### Citation

Thierry Barbot, Carlos Maquera. NIL-ANOSOV ACTIONS. This version contains a serious error which will will be corrected in the published version. 2015. 〈hal-01197491v2〉

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