Dynamics on PSL(2,C)-character varieties: 3-manifolds with toroidal boundary components

TL;DR

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

Contribution

It provides new analysis of the dynamics of automorphism actions on character varieties for hyperbolizable 3-manifolds with boundary, excluding interval bundles.

Findings

Characterization of the automorphism group's action dynamics

Identification of invariant subsets within the character variety

Insights into the geometric structures associated with these actions

Abstract

Let M be a compact, orientable, hyperbolizable 3-manifold with incompressible boundary which is not an interval bundle. We study the dynamics of the action of the outer automorphism group of the fundamental group of M on the relative PSL(2,C)-character variety.