Abstract
Let M be a hyperbolizable, nontrivial compression body without toroidal boundary components. In this paper, we characterize which discrete and faithful representations of the fundamental group of M into PSL(2,C) are separable-stable. The set of separable-stable representations forms a domain of discontinuity for the action of the outer automorphism group of the fundamental group of M on the PSL(2,C)-character variety of M.
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