Volume 15, issue 3 (2011)

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Minimal pseudo-Anosov translation lengths on the complex of curves

Geometry & Topology 15 (2011) 1297–1312
Abstract

We establish bounds on the minimal asymptotic pseudo-Anosov translation lengths on the complex of curves of orientable surfaces. In particular, for a closed surface with genus $g\ge 2$, we show that there are positive constants ${a}_{1}<{a}_{2}$ such that the minimal translation length is bounded below and above by ${a}_{1}∕{g}^{2}$ and ${a}_{2}∕{g}^{2}$.

Keywords
mapping class group, pseudo-Anosov map, complex of curves, Teichmüller
Mathematical Subject Classification 2010
Primary: 30F60, 32G15