Some new behaviour in the deformation theory of Kleinian groups

Abstract

We present examples of hyperbolizable 3-manifolds $M$ with the following property. Let $CC({\pi }_1(M))$ denote the space of convex co-compact representations of ${\pi }_1(M)$. We show that for every $K\ge 1$ there exists a representation $\rho$ in $\overline{CC({\pi }_1(M))}$ so that every $K$-quasiconformal deformation of $\rho$ lies in the closure of every component of $CC({\pi }_1(M))$. The examples $M$ were discovered by Anderson and Canary.

20 pages; 2 figures. To be published in Comm. in Anal and Geom