# Dynamics on the PSL(2, $\mathbb C$)-character variety of a twisted $I$-bundle

### Michelle Lee

University of Michigan, Ann Arbor, USA

## Abstract

Let $M$ be a twisted interval bundle over a closed nonorientable hyperbolizable surface. Let $\mathcal{X}(M)$ be the PSL(2, $\mathbb C$)-character variety of $\pi_1(M)$. We examine the dynamics of the action of Out$(\pi_1(M))$ on $\mathcal{X}(M),$ and in particular, we find an open set on which the action is properly discontinuous that is strictly larger than the interior of the deformation space of marked hyperbolic $3$-manifolds homotopy equivalent to $M$. Furthermore, we identify which discrete and faithful representations can lie in a domain of discontinuity for the action of Out$(\pi_1(M))$ on $\mathcal{X}(M)$.

## Cite this article

Michelle Lee, Dynamics on the PSL(2, $\mathbb C$)-character variety of a twisted $I$-bundle. Groups Geom. Dyn. 9 (2015), no. 1, pp. 187–201

DOI 10.4171/GGD/310