## Algebraic & Geometric Topology

### Uniform hyperbolicity of the curve graph via surgery sequences

#### 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.

#### Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513716042

Digital Object Identifier
doi:10.2140/agt.2014.14.3325

Mathematical Reviews number (MathSciNet)
MR3302964

Zentralblatt MATH identifier
1309.57015

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

#### Citation

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. https://projecteuclid.org/euclid.agt/1513716042

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