On the fundamental domain for the Teichmüller modular group (Q1271299)

The Teichmüller modular group \(\text{Mod}_p\) acts discontinuously on the Teichmüller space \({\mathcal T}_p\) of closed Riemann surfaces of genus \(p\). In [Invent. Math. 126, No. 2, 341-390 (1996; Zbl 0873.32018)] \textit{B. Maskit} described an explicit 1-1-correspondence between the points of \({\mathcal T}_p\) and oriented standard chains on closed Riemann surfaces of genus \(p\). The fundamental domain \(D_p\subset {\mathcal T}_p\) of the modular group is defined to be the set of minimal chains. The major result in this paper is that there are only finitely many elements \(\alpha\in\text{Mod}_p\) such that \(\alpha((\overline D_p) \cap \overline D_p\neq\emptyset\). It follows that one can divide the boundary of \(D_p\) into finitely many `sides', where theses sides are identified by elements of \(\text{Mod}_p\). The proof uses Buser's version of the Collar Lemma.