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

  • Michelle Lee

    University of Michigan, Ann Arbor, USA

Abstract

Let MM be a twisted interval bundle over a closed nonorientable hyperbolizable surface. Let X(M)\mathcal{X}(M) be the PSL(2, C\mathbb C)-character variety of π1(M)\pi_1(M). We examine the dynamics of the action of Out(π1(M))(\pi_1(M)) on X(M),\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 33-manifolds homotopy equivalent to MM. Furthermore, we identify which discrete and faithful representations can lie in a domain of discontinuity for the action of Out(π1(M))(\pi_1(M)) on X(M)\mathcal{X}(M).

Cite this article

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

DOI 10.4171/GGD/310