3/27/2008

Ian Biringer
University of Chicago

Sequences of Hyperbolic 3-Manifolds with Unfaithful Markings

Let Gamma be a finitely generated group. To every representation rho: \Gamma \to Isom (\BH3) with discrete and torsion-free image there corresponds a hyperbolic 3-manifold M_\rho = \BH3 / \rho (\Gamma). I will present some new results linking the pointwise convergence of a sequence of such representations with Gromov-Hausdorff convergence of the corresponding quotient manifolds. A detailed analysis already exists for sequences of faithful representations; I will give examples that illustrate the failure of these theorems in the unfaithful setting, and offer some useful replacements. Joint work with Juan Souto.