Constructing proper affine actions via higher strip deformations

Abstract

We introduce higher strip deformations, which give a way of constructing affine deformations of discrete free groups in the image of the irreducible representation ${\mathrm{PSL}}_2\mathbb{R}\to \mathrm{SO}(2n,2n-1)$. We use the Margulis invariant to find a properness condition for these deformations, showing that each convex cocompact free group admits affine deformations acting properly on ${\mathbb{R}}^{4n-1}$. Using our method we can also construct proper affine actions of virtually free groups, which we demonstrate by finding proper actions of $C_2\star C_3$ on ${\mathbb{R}}^7.$

arXiv comment22 pages, 16 figures