Uniform hyperbolicity of the curve graph via surgery sequences

Abstract

We prove that the curve graph ${\mathcal{C}}^{\left(1\right)}\left(S\right)$ 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.