On the quasi-isometric rigidity of graphs of surface groups

2019/04/23 by Alexander Taam, Taam, Alexander, Nicholas Touikan +1 · 1 citation
Mathematics · #20E08 #20F67 #22E40 #57M12 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1904.10482

openalex publication_date 2019/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Γ be a word hyperbolic group with a cyclic JSJ decomposition that has only rigid vertex groups, which are all fundamental groups of closed surface groups. We show that any group H quasi-isometric to Γ is abstractly commensurable with Γ.

Citations

• Quasi-isometries between groups with two-ended splittings

Cited by

• On the proofs of Leighton's Graph Covering Theorem, a notion dual to commensurability, and normal virtual retracts

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