Incommensurable lattices in Baumslag–Solitar complexes.

This paper concerns locally finite 2‐complexes Xm,n$X_{m,n}$ that are combinatorial models for the Baumslag–Solitar groups BS(m,n)$BS(m,n)$. We show that, in many cases, the locally compact group Aut(Xm,n)$\operatorname{Aut}(X_{m,n})$ contains incommensurable uniform lattices. The lattices we construct also admit isomorphic Cayley graphs and are finitely presented, torsion‐free, and coherent. [ABSTRACT FROM AUTHOR]