Convergence and divergence of Kleinian surface groups
  We characterize sequences of Kleinian surface groups with convergent subsequences in terms of the asymptotic behavior of the ending invariants of the associated hyperbolic 3-manifolds. Asymptotic behavior of end invariants in a convergent sequence predicts the parabolic locus of the algebraic limit as well as how the algebraic limit wraps within the geometric limit under the natural locally isometric covering map. 
Jeffrey Brock, Kenneth Bromberg, Richard Canary and Cyril Lecuire
math.GT