Convergence and divergence of Kleinian punctured torus groups

Details Convergence and divergence of Kleinian punctured torus groups Convergence and divergence of Kleinian punctured torus groups

2007-01-12

arxiv.org/abs/math/0701342v2

Mathematics

Geometric Topology

30 pages v2: The proof of Theorem 3.8 in v1 is rewritten by using elementary arguments so that we do not make use of the Drill

Scientific paper

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. 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 geometric limits of sequences of Bers slices.

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