2020/07/20 by Sam O. Shepherd, Sam Shepherd, Shepherd, Sam +2 · 3 citations
Computer Science · Mathematics · #20F65 (Primary) 20E08 #57M10 (Secondary) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR #msc:20E08 #msc:20F65 #msc:57M10 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2007.10034
53 pages, 3 figures; v2: minor changes including to the statement of Theorem 1.3; v3: minor changes following referee's comments; to appear in Crelles
openalex publication_date 2020/07/20 · openalex created_date 2020/07/23 · arxiv created 2021/10/27 · arxiv updated 2021/10/29 · openalex updated_date 2026/07/28
We study the quasi-isometric rigidity of a large family of finitely generated groups that split as graphs of groups with virtually free vertex groups and two-ended edge groups. Let G be a group that is one-ended, hyperbolic relative to virtually abelian subgroups, and has JSJ decomposition over two-ended subgroups containing only virtually free vertex groups that aren't quadratically hanging. Our main result is that any group quasi-isometric to G is abstractly commensurable to G. In particular, our result applies to certain "generic" HNN extensions of a free group over cyclic subgroups.