arXiv
Open Access
2022
Commensurability of lattices in right-angled buildings
Sam Shepherd
Abstrak
Let $Γ$ be a graph product of finite groups, with finite underlying graph, and let $Δ$ be the associated right-angled building. We prove that a uniform lattice $Λ$ in the cubical automorphism group Aut$(Δ)$ is weakly commensurable to $Γ$ if and only if all convex subgroups of $Λ$ are separable. As a corollary, any two finite special cube complexes with universal cover $Δ$ have a common finite cover. An important special case of our theorem is where $Γ$ is a right-angled Coxeter group and $Δ$ is the associated Davis complex. We also obtain an analogous result for right-angled Artin groups. In addition, we deduce quasi-isometric rigidity for the group $Γ$ when $Δ$ has the structure of a Fuchsian building.
Topik & Kata Kunci
Penulis (1)
S
Sam Shepherd
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2022
- Bahasa
- en
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- arXiv
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- Open Access ✓