Simple Lattices in Products of Davis Complexes

Abstract

Burger and Mozes (1997) constructed the first examples of simple uniform lattices in products of trees. In this paper, we construct simple uniform lattices in products of certain Davis complexes. More precisely, we consider lattices in products of trees and two-dimensional Davis complexes of the right-angled Coxeter group whose defining graph is an odd graph. As part of the proof, we define an analogue of the Burger-Mozes universal groups in this setting, and provide a local criterion for a vertex transitive group to be dense in the universal group.