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

2011/03/17 by Michelle Lee, Lee, Michelle
Biochemistry, Genetics and Molecular Biology · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Microtubule and mitosis dynamics #math.GT

paper · pdf · doi:10.48550/arxiv.1103.3479

arxiv created 2011/03/17 · openalex publication_date 2011/03/17 · arxiv updated 2011/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a twisted interval bundle over a nonorientable hyperbolizable surface. Let X(M) be the PSL(2,C)-character variety of π₁(M). We examine the dynamics of the action of Out(π₁(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(π₁(M)) on X(M).

Citations

• On dynamics of Out(F_n) on PSL(2,C) characters

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