#### 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