Event time:

Thursday, February 28, 2008 - 11:30am to Wednesday, February 27, 2008 - 7:00pm

Location:

431 DL

Speaker:

Ian Biringer

Speaker affiliation:

Chicago

Event description:

Let $\Gamma $ be a finitely generated group. To every representation $\rho

: \Gamma \to Isom ({\bf H}^3) $ with discrete and torsion-free image there

corresponds a hyperbolic $3$-manifold $M_\rho = {\bf H}^3 / \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.