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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 C(1)(S) 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
Mathematical Subject Classification 2010
Primary: 57M99
Secondary: 30F60
References
Publication
Received: 16 July 2013
Revised: 24 April 2014
Accepted: 25 April 2014
Published: 15 January 2015
Authors
Matt Clay
Department of Mathematical Sciences
University of Arkansas
SCEN 309
Fayetteville, AR 72701
USA
http://comp.uark.edu/~mattclay
Kasra Rafi
Department of Mathematics
University of Toronto
Room 6290
40 St. George Street
Toronto, Ontario M5S 2E4
Canada
http://www.math.toronto.edu/~rafi/
Saul Schleimer
Mathematics Institute
University of Warwick
Zeeman Building
Conventry CV4 7AL
UK
http://homepages.warwick.ac.uk/~masgar/