COMPLEX FENCHEL-NIELSEN COORDINATES FOR QUASI-FUCHSIAN STRUCTURES

Abstract

Let F g be a closed oriented surface of genus g ≥ 2 and let [Formula: see text] be the space of marked quasi-fuchsian structures on F g . Let [Formula: see text] be a set of non-intersecting, non-trivial simple closed curves on F g that cuts F g into pairs of pants components. In this note, we construct global complex coordinates for [Formula: see text] relative to [Formula: see text] giving an embedding of [Formula: see text] into [Formula: see text]. The totally real subspace of [Formula: see text] with respect to these coordinates is the Teichmüller Space [Formula: see text] of marked hyperbolic structures on F g , the coordinates reduce to the usual Fenchel-Nielsen coordinates for [Formula: see text] relative to [Formula: see text]. Various properties of the embedded image are studied.