Algebraic & Geometric Topology

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

Michelle Lee

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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.

Article information

Algebr. Geom. Topol., Volume 14, Number 4 (2014), 2149-2179.

Received: 2 July 2013
Revised: 24 October 2013
Accepted: 26 October 2013
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57M60: Group actions in low dimensions

compression body hyperbolic $3$–manifold character variety outer automorphism group


Lee, Michelle. Dynamics on the $\mathrm{PSL}(2,\mathbb{C})$–character variety of a compression body. Algebr. Geom. Topol. 14 (2014), no. 4, 2149--2179. doi:10.2140/agt.2014.14.2149.

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