A deformation of Penner's simplicial coordinate

Abstract

We produce a one-parameter family of coordinates $\{{\Psi }_h{\}}_{h\in \mathbb{R}}$ of the decorated Teichmüller 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 $h⩾0$, 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 $P_h(T)\subset P_{h^{\prime }}(T)$ if $h<h^{\prime }$. As a consequence, Bowditch-Epstein and Penner's cell decomposition of the decorated Teichmüller space is reproduced.

19 pages, 6 figures

References in corpus (2)

• Rigidity of Polyhedral Surfaces
• Cell decompositions of Teichmüller spaces of surfaces with boundary