Final Activity Report Summary - DISCRETE GROUPS (Structures of spaces of complex hyperbolic discrete groups)
Two major achievements of this project are, first, the construction of an open set of maximal dimension inside the complex hyperbolic quasi-Fuchsian space and, secondly, the construction of a real analytic structure on a subset of the representation space containing quasi-Fuchsian space. The first of these goals was achieved by constructing a flexible fundamental domain for groups in the neighbourhood of R-Fuchsian space. The second was achieved by exhibiting coordinates that generalise the classical Fenchel-Nielsen coordinates on Teichmueller space.