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

Lee, Michelle

doi:10.2140/agt.2014.14.2149

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Dynamics on the $\mathrm{PSL}(2,\mathbb{C})$–character variety of a compression body

Michelle Lee

Algebraic & Geometric Topology 14 (2014) 2149–2179

DOI: 10.2140/agt.2014.14.2149

Abstract

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Let $M$ be a nontrivial compression body without toroidal boundary components. Let $X (M)$ be the $PSL (2, ℂ)$ –character variety of $π_{1} (M)$ . We examine the dynamics of the action of $Out (π_{1} (M))$ 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 $3$ –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/

Volume 14, issue 4 (2014)