## Algebraic & Geometric Topology

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

Michelle Lee

#### Abstract

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 $M$.

#### Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715961

Digital Object Identifier
doi:10.2140/agt.2014.14.2149

Mathematical Reviews number (MathSciNet)
MR3331612

Zentralblatt MATH identifier
1307.57013

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

#### Citation

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. https://projecteuclid.org/euclid.agt/1513715961

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