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November 2011 A deformation of Penner's simplicial coordinate
Tian Yang
J. Differential Geom. 89(3): 529-551 (November 2011). DOI: 10.4310/jdg/1335207377

Abstract

We find a one-parameter family of coordinates $\{\Psi_h\}_{h\in\mathbb{R}}$ which is a deformation of Penner's simplicial coordinate of the decorated Teichmüller space of an ideally triangulated punctured surface $(S, T)$ of negative Euler characteristic. If $h \ge 0$, the decorated Teichmüller space in the $\Psi_h$ coordinate becomes an explicit convex polytope $P(T)$ independent of $h$, and if $h < 0$, the decorated Teichmüller space becomes an explicit bounded convex polytope $P_h(T)$ so that $P_h(T)\subset P_{h'} (T)$ if $h < h'$. As a consequence, Bowditch-Epstein and Penner's cell decomposition of the decorated Teichmüller space is reproduced.

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Tian Yang. "A deformation of Penner's simplicial coordinate." J. Differential Geom. 89 (3) 529 - 551, November 2011. https://doi.org/10.4310/jdg/1335207377

Information

Published: November 2011
First available in Project Euclid: 23 April 2012

zbMATH: 1258.30020
MathSciNet: MR2879250
Digital Object Identifier: 10.4310/jdg/1335207377

Rights: Copyright © 2011 Lehigh University

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Vol.89 • No. 3 • November 2011
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