Geometry & Topology
- Geom. Topol.
- Volume 17, Number 5 (2013), 2855-2875.
Uniform hyperbolicity of the graphs of curves
Let denote the curve complex of the closed orientable surface of genus with punctures. Masur and Minksy and subsequently Bowditch showed that is –hyperbolic for some . In this paper, we show that there exists some independent of such that the curve graph is –hyperbolic. Furthermore, we use the main tool in the proof of this theorem to show uniform boundedness of two other quantities which a priori grow with and : the curve complex distance between two vertex cycles of the same train track, and the Lipschitz constants of the map from Teichmüller space to sending a Riemann surface to the curve(s) of shortest extremal length.
Geom. Topol., Volume 17, Number 5 (2013), 2855-2875.
Received: 16 January 2013
Revised: 27 May 2013
Accepted: 3 July 2013
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 05C12: Distance in graphs 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 57M07: Topological methods in group theory 57M15: Relations with graph theory [See also 05Cxx] 57M20: Two-dimensional complexes
Aougab, Tarik. Uniform hyperbolicity of the graphs of curves. Geom. Topol. 17 (2013), no. 5, 2855--2875. doi:10.2140/gt.2013.17.2855. https://projecteuclid.org/euclid.gt/1513732689