Algebraic & Geometric Topology

Uniform hyperbolicity of the curve graph via surgery sequences

Matt Clay, Kasra Rafi, and Saul Schleimer

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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.

Article information

Algebr. Geom. Topol., Volume 14, Number 6 (2014), 3325-3344.

Received: 16 July 2013
Revised: 24 April 2014
Accepted: 25 April 2014
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M99: None of the above, but in this section
Secondary: 30F60: Teichmüller theory [See also 32G15]

curve complex arc complex Gromov hyperbolic


Clay, Matt; Rafi, Kasra; Schleimer, Saul. Uniform hyperbolicity of the curve graph via surgery sequences. Algebr. Geom. Topol. 14 (2014), no. 6, 3325--3344. doi:10.2140/agt.2014.14.3325.

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