Incommensurable lattices in Baumslag–Solitar complexes

Abstract

AbstractThis paper concerns locally finite 2‐complexes that are combinatorial models for the Baumslag–Solitar groups . We show that, in many cases, the locally compact group contains incommensurable uniform lattices. The lattices we construct also admit isomorphic Cayley graphs and are finitely presented, torsion‐free, and coherent.