Dynamics on PSL(2, $\mathbb{C}$)-character varieties: 3-manifolds with toroidal boundary components

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 Out(${\pi }_1(M$)) on the relative PSL(2, $\mathbb{C}$)-character variety $X_T(M)$.