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

### James W. Anderson and Richard D. Canary

## Abstract

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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On 23 Nov 1999, 17:36.