Uniform hyperbolicity of the graphs of curves

作者：Aougab Tarik^*

来源：Geometry and Topology, 2013, 17(5): 2855-2875.

DOI：10.2140/gt.2013.17.2855

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 delta-hyperbolic for some delta = delta(g. p) In this paper, we show that there exists some delta > 0 independent of g, p such that the curve graph C-1 (Sg,p) is delta-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 Teichmuller space to C(S) sending a Riemann surface to the curve(s) of shortest extremal length.

• 出版日期2013