Parameters for generalized Teichmüller spaces

Abstract

We give a finite number of real parameters for the Teichmüller space of a hyperbolic pair of pants with a conical singularity. We also give a finite number of real parameters for a space of hyperbolic structures on a class of 2-dimensional simplicial complexes. Such a space of hyperbolic structures associated to a simplicial complex can be regarded as a Teichmüller space for that complex.