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

TL;DR

This paper investigates how the outer automorphism group of a compression body's fundamental group acts dynamically on its PSL(2,C)-character variety, revealing insights into the geometric structures of such 3-manifolds.

Contribution

It provides new analysis of the dynamics of automorphism groups on character varieties specifically for nontrivial compression bodies without toroidal boundaries.

Findings

Characterization of the automorphism group's action dynamics

Identification of invariant subsets within the character variety

Insights into the geometric structures associated with compression bodies

Abstract

Let M be a nontrivial compression body without toroidal boundary components. We study the dynamics of the group of outer automorphisms of the fundamental group of M on the PSL(2,C)-character variety of M.