Incommensurable lattices in Baumslag-Solitar complexes

Max Forester

doi:10.1112/jlms.12879

Incommensurable lattices in Baumslag-Solitar complexes

Group Theory 2024-03-14 v2 Geometric Topology

Authors: Max Forester

View on arXiv ↗ PDF ↗ DOI ↗

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.

Keywords

baumslag-solitar complexes locally compact groups uniform lattices incommensurable lattices cayley graphs coherent groups

Cite

@article{arxiv.2207.14703,
  title  = {Incommensurable lattices in Baumslag-Solitar complexes},
  author = {Max Forester},
  journal= {arXiv preprint arXiv:2207.14703},
  year   = {2024}
}

Comments

v2: 34 pages. The notion of depth profile has been modified slightly to exclude elliptic elements. There is some new exposition with additional references

Incommensurable lattices in Baumslag-Solitar complexes

Abstract

Keywords

Cite

Comments

Related papers