Hyperbolic relatively hyperbolic graphs and disc graphs

Abstract

We show that a relatively hyperbolic graph with uniformly hyperbolic peripheral subgraphs is hyperbolic. As an application, we show that the disc graph and the electrified disc graph of a handlebody H of genus g>1 are hyperbolic, and we determine their Gromov boundaries.

Small corrections and clarifications

References in corpus (4)

• Train tracks and the Gromov boundary of the complex of curves
• On metric relative hyperbolicity
• Slim unicorns and uniform hyperbolicity for arc graphs and curve graphs
• Hyperbolicity of the graph of non-separating multicurves