# Proper affine actions of right angled Coxeter groups

## Proper affine actions of right angled Coxeter groups - Jeffery Danciger

Jeffrey Danciger
University of Texas, Austin
March 8, 2016
We prove that any right-angled Coxeter group on $k$ generators admits a proper action by affine transformations on $\mathbb R^{k(k-1)/2}$. As a corollary, many interesting groups admit proper affine actions including surface groups, hyperbolic three-manifold groups, and Gromov hyperbolic groups of arbitrarily large virtual cohomological dimension. Joint work with Francois Gueritaud and Fanny Kassel.