Infinitely many commensurability classes of compact Coxeter polyhedra in ${\mathbb{H}}^4$ and ${\mathbb{H}}^5$

Abstract

We prove that certain families of compact Coxeter polyhedra in 4- and 5-dimensional hyperbolic space constructed by Makarov give rise to infinitely many commensurability classes of reflection groups in these dimensions.

Final version, to appear in Advances in Mathematics