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 $\ddot{I}$ of a word hyperbolic group is affine Anosov if and only if its linear part ${\mathtt{L}}_{\ddot{I}}$ is Anosov in ${\mathsf{SO}}^0(n+1,n)$ with respect to the stabilizer of a maximal isotropic plane and $\ddot{I}(\hat{I}“)$ acts properly on ${\mathbb{R}}^{2n+1}$.

25 pages, Minor changes