Uniform hyperbolicity of the curve graphs

Brian H. Bowditch

Vol. 269 (2014), No. 2, 269–280

DOI: 10.2140/pjm.2014.269.269

Abstract

We show that there is a universal constant, $k$, such that the curve graph associated to any compact orientable surface is $k$-hyperbolic. Independent proofs of this have been given by Aougab, by Hensel, Przytycki and Webb, and by Clay, Rafi and Schleimer.

Keywords

uniform hyperbolicity, curve graph, surface

Mathematical Subject Classification 2010

Primary: 20F65

Milestones

Received: 8 March 2013

Revised: 24 June 2013

Accepted: 28 June 2013

Published: 26 July 2014