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Trees of Graphs as Boundaries of Hyperbolic Groups

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arxiv 2312.15827 v2 pith:2XRV7RJH submitted 2023-12-25 math.GR

Nima Hoda , Jacek Świątkowski This is my paper · ORCID
classification math.GR
keywords groupsboundariesgraphsendedgromovhyperbolicsplittingtrees
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We characterize those 1-ended word hyperbolic groups whose Gromov boundaries are homeomorphic to trees of graphs (i.e. to inverse limits of graphs that have particularly simple finitary descriptions). These are groups with the simplest connected Gromov boundaries of topological dimension 1. The characterization is expressed in terms of algebraic properties of the Bowditch JSJ splitting of the corresponding groups (i.e. the canonical JSJ splitting over 2-ended subgroups).

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Conformal dimension bounds, Pontryagin sphere boundaries, and algebraic fibering of right-angled Coxeter groups

    math.GR 2025-10 conditional novelty 7.0 of 10

    (n,m)-branching graphs give right-angled Coxeter groups with boundary conformal dimension at least 1 + log n/log(3m-7), yielding infinitely many quasi-isometry classes with Pontryagin sphere boundary and with virtual ...

  2. Visual metrics on boundaries of hyperbolic spaces

    math.GT 2025-06 conditional novelty 2.0 of 10

    An expository article on visual metrics on boundaries of hyperbolic spaces, quasisymmetries, conformal dimension, and round trees.

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