Global real analytic angle parameters for Teichmüller spaces (Q1389864)

A Fuchsian group \(G\) acting on the unit disk \(D\) is of type \((g,0,m)\), if the quotient space \(D/G\) is a Riemann surface of genus \(g\) with \(m\) holes. It is supposed that \(2g +m \geq 3\). The Teichmüller space \(T(g,0,m)\) of marked Fuchsian groups of type \((g, 0,m)\) can be parametrized global real analytically by lengths of closed geodesics and by intersection angles between geodesics on a Riemann surface represented by a marked Fuchsian group. Let \(N_1 (g,0,m)\) be the minimal numbers of length parameters and \(N_2 (g,0,m)\) the minimal number of angle parameters which describe \(T(g,0,m)\). It is known that \(N_1(g,0,0)= \dim(T(g,0,0)) +1\). In this paper the author obtains global real analytic angle parameters for \(T(1,0,1)\) and \(T(2,0,0)\). He also shows that \(N_2(1,0,1)= \dim(T(1,0,1))\) and \(N_2(2,0,0) \leq\dim (T(2,0,0))+1\).