Affine Anosov representations and proper actions

Abstract

We define the notion of affine Anosov representations of word hyperbolic groups into the affine group ${\mathsf{SO}}^0(n+1,n)⋉{\mathbb{R}}^{2n+1}$. We then show that a representation $\rho$ of a word hyperbolic group is affine Anosov if and only if its linear part ${\mathtt{L}}_{\rho }$ is Anosov in ${\mathsf{SO}}^0(n+1,n)$ with respect to the stabilizer of a maximal isotropic plane and $\rho (\Gamma )$ acts properly on ${\mathbb{R}}^{2n+1}$.

25 pages, Minor changes

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Cited by in corpus (2)

• Margulis Multiverse: Infinitesimal Rigidity, Pressure Form and Convexity
• Affine actions with Hitchin linear part