Complex hyperbolic Fenchel-Nielsen coordinates

Let Sigma be a closed, orientable surface of genus g. It is known that the SU(2, 1) representation variety of pi(1)(Sigma) has 2g - 3 components of (real) dimension 16g - 16 and two components of dimension 8g - 6. Of special interest are the totally loxodromic, faithful (that is quasi-Fuchsian) representations. In this paper we give global real analytic coordinates on a subset of the representation variety that contains the quasi-Fuchsian representations. These coordinates are a natural generalisation of Fenchel-Nielsen coordinates on the Teichmuller space of Sigma and complex Fenchel - Nielsen coordinates on the (classical) quasi-Fuchsian space of Sigma. (C) 2007 Elsevier Ltd. All rights reserved.