Some new behaviour in the deformation theory of Kleinian groups

Details Some new behaviour in the deformation theory of Kleinian groups Some new behaviour in the deformation theory of Kleinian groups

2000-10-16

arxiv.org/abs/math/0010164v1

Mathematics

Geometric Topology

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

Scientific paper

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 $K\geq 1$ there exists a representation $\rho$ in $\bar {CC(\pi_1(M))}$ 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.

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