Infinite generation of non-cocompact lattices on right-angled buildings

Anne Thomas and Kevin Wortman

Abstract

Let $\mathrm{\Gamma }$ be a non-cocompact lattice on a locally finite regular right-angled building $X$. We prove that if $\mathrm{\Gamma }$ has a strict fundamental domain then $\mathrm{\Gamma }$ is not finitely generated. We use the separation properties of subcomplexes of $X$ called tree-walls.