Cores of hyperbolic 3-manifolds and limits of Kleinian groups II

James W. Anderson and Richard D. Canary


In this note, we continue the investigation of the relationship between algebraic and geometric limits of sequences of Kleinian groups begun in the first paper of this series.

We study the conjecture that the algebraic and geometric limits of an algebraically convergent sequence of isomorphic Kleinian groups agree if there are no new parabolics in the algebraic limit. We prove that this conjecture holds in ``most'' cases for type-preserving sequences of Kleinian groups. In particular, we show that it holds when the domain of discontinuity of the algebraic limit of such a sequence is non-empty. We further show, with the same assumptions, that the limit sets of the groups in the sequence converge to the limit set of the algebraic limit. As a corollary, we verify the conjecture for finitely generated Kleinian groups which are not (non-trivial) free products of surface groups and infinite cyclic groups

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