Dynamics on the PSL(2, ℂ)–character variety of a compression body

Lee, Michelle¹

¹Mathematics Building, University of Maryland, College Park, MD 20742, USA

Algebraic and Geometric Topology, Tome 14 (2014) no. 4, pp. 2149-2179

Résumé

Let M be a nontrivial compression body without toroidal boundary components. 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 3–manifolds homotopy equivalent to M.

Détail

DOI : 10.2140/agt.2014.14.2149

Classification : 57M50, 57M60
Keywords: compression body, hyperbolic $3$–manifold, character variety, outer automorphism group

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