2021/11/26 by J. O. Button, Button, J. O.
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2111.13427
openalex publication_date 2021/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A group with a geometric action on some hyperbolic space is necessarily word hyperbolic, but on the other hand every countable group acts (metrically) properly by isometries on a locally finite hyperbolic graph. In this paper we consider what happens when a group acts isometrically on a restricted class of hyperbolic spaces, for instance quasitrees. We obtain strong conclusions on the group structure if the action has a locally finite orbit, especially if the group is finitely generated. We also look at group actions on finite products of quasitrees, where our actions may be by automorphisms or by isometries, including the Leary - Minasyan group.