Convergence and divergence of Kleinian punctured torus groups

In this paper we give a necessary and sufficient condition in which a sequence of Kleinian punctured torus groups converges. This result tells us that every exotically convergent sequence of Kleinian punctured torus groups is obtained by the method due to Anderson and Canary (Invent. Math. 1996). Thus we obtain a complete description of the set of points at which the space of Kleinian punctured torus groups self-bumps. We also discuss Hausdorff limits of sequences of Bers slices.