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

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

2011-03-17

arxiv.org/abs/1103.3479v1

Mathematics

Geometric Topology

Scientific paper

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

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