Groups, Geometry, and Dynamics

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Volume 10, Issue 1, 2016, pp. 365–405
DOI: 10.4171/GGD/352

Published online: 2016-02-09

Hyperbolic relatively hyperbolic graphs and disk graphs

Ursula Hamenstädt[1]

(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