Volume 14, issue 6 (2014)

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Uniform hyperbolicity of the curve graph via surgery sequences

Matt Clay, Kasra Rafi and Saul Schleimer

Algebraic & Geometric Topology 14 (2014) 3325–3344
Abstract

We prove that the curve graph ${\mathsc{C}}^{\left(1\right)}\left(S\right)$ is Gromov-hyperbolic with a constant of hyperbolicity independent of the surface $S$. The proof is based on the proof of hyperbolicity of the free splitting complex by Handel and Mosher, as interpreted by Hilion and Horbez.

Keywords
curve complex, arc complex, Gromov hyperbolic
Primary: 57M99
Secondary: 30F60