Dynamics on PSL(2,C)-character varieties: 3-manifolds with toroidal   boundary components
  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. 
Richard Canary and Aaron Magid
math.GT