A deformation of Penner's simplicial coordinate

Details A deformation of Penner's simplicial coordinate A deformation of Penner's simplicial coordinate

2010-11-07

arxiv.org/abs/1011.1615v3

J Differential Geom. 89 (2011) 529-551

Mathematics

Geometric Topology

19 pages, 6 figures

Scientific paper

We produce a one-parameter family of coordinates $\{\Psi_h\}_{h\in\mathbb{R}}$ of the decorated Teichm\"{u}ller space of an ideally triangulated punctured surface $(S,T)$ with negative Euler characteristic, which is a deformation of Penner's simplicial coordinate \cite{P1}. If $h\geqslant0$, the decorated Teichm\"{u}ller space in the $\Psi_h$ coordinate becomes an explicit convex polytope $P(T)$ independent of $h$, and if $h<0$, the decorated Teichm\"{u}ller space becomes an explicit bounded convex polytope $P_h(T)$ so that $P_h(T)\subset P_{h'}(T)$ if $h

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