Cell decompositions of Teichmüller spaces of surfaces with boundary

Abstract

A family of coordinates ${\psi }_h$ for the Teichmüller space of a compact surface with boundary was introduced in \cite{l2}. In the work \cite{m1}, Mondello showed that the coordinate ${\psi }_0$ can be used to produce a natural cell decomposition of the Teichmüller space invariant under the action of the mapping class group. In this paper, we show that the similar result also works for all other coordinate ${\psi }_h$ for any $h\ge 0$.

arXiv comment11 pages, 6 figures

References in corpus (1)

• Rigidity of Polyhedral Surfaces

Cited by in corpus (1)

• A deformation of Penner's simplicial coordinate