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arXiv · 2207.14703

Incommensurable lattices in Baumslag-Solitar complexes

Max Forester
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Abstract

This paper concerns locally finite 2-complexes $X_{m,n}$ which are combinatorial models for the Baumslag-Solitar groups $BS(m,n)$. We show that, in many cases, the locally compact group 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.

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Max Forester. 2022-07-29. Incommensurable lattices in Baumslag-Solitar complexes. https://doi.org/10.1112/jlms.12879

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