Algebraic & Geometric Topology

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

Michelle Lee

Full-text: Open access

Abstract

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

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

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

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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