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arXiv · 1509.03816

Nil-Anosov actions

Thierry Barbot·Carlos Maquera
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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 Theoremfor such an action when the group $G$ is nilpotent. Finally, we focus on the case where $G$ is nilpotent andthe unstable bundle has codimension one. We prove that in this case the action is a Nil-extensionover 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.

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Thierry Barbot, Carlos Maquera. 2015-09-13. Nil-Anosov actions. https://arxiv.org/abs/1509.03816

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