Volume 17, issue 5 (2013)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Uniform hyperbolicity of the graphs of curves

Tarik Aougab

Geometry & Topology 17 (2013) 2855–2875
Abstract

Let C(Sg,p) denote the curve complex of the closed orientable surface of genus g with p punctures. Masur and Minksy and subsequently Bowditch showed that C(Sg,p) is δ–hyperbolic for some δ = δ(g,p). In this paper, we show that there exists some δ > 0 independent of g,p such that the curve graph C1(Sg,p) is δ–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 g and p: the curve complex distance between two vertex cycles of the same train track, and the Lipschitz constants of the map from Teichmüller space to C(S) sending a Riemann surface to the curve(s) of shortest extremal length.

Keywords
uniform hyperbolicity, curve complex, mapping class group
Mathematical Subject Classification 2010
Primary: 05C12, 20F65, 57M07, 57M15, 57M20
References
Publication
Received: 16 January 2013
Revised: 27 May 2013
Accepted: 3 July 2013
Published: 14 October 2013
Proposed: Danny Calegari
Seconded: Jean-Pierre Otal, Walter Neumann
Authors
Tarik Aougab
Department of Mathematics
Yale University
10 Hillhouse Avenue
New Haven, CT 06510
USA