Groups, Geometry, and Dynamics


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Volume 9, Issue 1, 2015, pp. 187–201
DOI: 10.4171/GGD/310

Published online: 2015-04-28

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

Michelle Lee[1]

(1) University of Michigan, Ann Arbor, USA

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 $\mathcal{X}(M)$.

Keywords: Twisted interval bundle, hyperbolic 3-manifold, character variety, outer automorphism group

Lee Michelle: Dynamics on the PSL(2, $\mathbb C$)-character variety of a twisted $I$-bundle. Groups Geom. Dyn. 9 (2015), 187-201. doi: 10.4171/GGD/310