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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Dynamics on the $\mathrm{PSL}(2,\mathbb{C})$–character variety of a compression body

Michelle Lee

Algebraic & Geometric Topology 14 (2014) 2149–2179
Abstract
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Let M be a nontrivial compression body without toroidal boundary components. Let X(M) be the PSL(2, )–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.

Keywords
compression body, hyperbolic $3$–manifold, character variety, outer automorphism group
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 57M60
References
Publication
Received: 2 July 2013
Revised: 24 October 2013
Accepted: 26 October 2013
Published: 28 August 2014
Authors
Michelle Lee
Mathematics Building
University of Maryland
College Park, MD 20742
USA
http://www2.math.umd.edu/~mdl/