Algebraic & Geometric Topology

Uniform hyperbolicity of the curve graph via surgery sequences

Matt Clay, Kasra Rafi, and Saul Schleimer

Full-text: Open access

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]

Keywords
curve complex arc complex Gromov hyperbolic

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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References

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