Commensurability of lattices in right-angled buildings

DOI10.1016/j.aim.2024.109522arXiv2203.01210MaRDI QIDQ6200726

Sam Shepherd

Publication date: 25 March 2024

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.01210

zbMATH Keywords

Coxeter groupscommensurabilityquasi-isometric rigidityright-angled buildingDavis complexspecial cube complexes

Mathematics Subject Classification ID

Covering spaces and low-dimensional topology (57M10) Geometric group theory (20F65) Reflection and Coxeter groups (group-theoretic aspects) (20F55)

Cites Work

• The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning).
• Groups generated by reflections and aspherical manifolds not covered by Euclidean space
• Commensurability and separability of quasiconvex subgroups.
• Finite index subgroups of graph products.
• Finite common coverings of graphs
• Right-angled Artin groups are commensurable with right-angled Coxeter groups
• Rigidity of quasi-isometries for some hyperbolic buildings
• Commensurability of groups quasi-isometric to RAAGs
• When is the graph product of hyperbolic groups hyperbolic?
• Two generalisations of Leighton's theorem (with an appendix by Giles Gardam and Daniel J. Woodhouse)
• Leighton's theorem : extensions, limitations and quasitrees
• The nonexistence of certain generalized polygons
• Special cube complexes
• Tree-graded spaces and asymptotic cones of groups. (With an appendix by Denis Osin and Mark Sapir).
• Subgroup separability of the figure 8 knot group.
• Quasi-isometric rigidity of Fuchsian buildings
• Erratum to ``Buildings with isolated subspaces and relatively hyperbolic Coxeter groups.
• An introduction to right-angled Artin groups.
• Finitely presented simple groups and products of trees
• Geometric Group Theory
• Revisiting Leighton’s theorem with the Haar measure
• Quasi-isometric rigidity of a class of right-angled Coxeter groups
• Lattices in 𝑃𝑈(𝑛,1) that are not profinitely rigid
• Strong Rigidity of Locally Symmetric Spaces. (AM-78)
• On hyperbolic buildings
• On cubulated relatively hyperbolic groups
• Leighton's theorem and regular cube complexes
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