Cell decompositions of Teichmüller spaces of surfaces with boundary

Abstract

A family of coordinates $ψ_h$ 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 $ψ_0$ 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 $ψ_h$ for any $h \geq 0$.

11 pages, 6 figures