Groups, Geometry, and Dynamics
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Published online: 2016-02-09
Hyperbolic relatively hyperbolic graphs and disk graphsUrsula Hamenstädt (1) Universität Bonn, Germany
We show that a relatively hyperbolic graph with uniformly hyperbolic peripheral subgraphs is hyperbolic. As an application, we show that the disk graph and the electrified disk graph of a handlebody $H$ of genus $g \geq 2$ are hyperbolic, and we determine their Gromov boundaries.
Keywords: Hyperbolicity, relatively hyperbolic graph, handlebody, disk graph
Hamenstädt Ursula: Hyperbolic relatively hyperbolic graphs and disk graphs. Groups Geom. Dyn. 10 (2016), 365-405. doi: 10.4171/GGD/352