Abstract: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 a… Show more
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