Thin right-angled Coxeter groups in some uniform arithmetic lattices

Abstract

Using a variant of an unpublished argument due to Agol, we show that an irreducible right-angled Coxeter group on $n\ge 3$ vertices embeds as a thin subgroup of a uniform arithmetic lattice in an indefinite orthogonal group $\mathrm{O}(p,q)$ for some $p,q\ge 1$ satisfying $p+q=n$.

arXiv comment4 pages