Cores of hyperbolic 3-manifolds and limits of Kleinian groups

Abstract. We study the relationship between the algebraic and geometric limits of a sequence of isomorphic Kleinian groups. We prove that, with certain restrictions on the algebraic limit, the alge-braic limit is the fundamental group of a compact submanifold of the quotient of the geometric limit. In particular, we show that the algebraic and geometric limits agree, in the absence of parabolics, if the algebraic limit either has nonempty domain of discontinuity or is not isomorphic to a nontrivial free product of (orientable) surface groups and cyclic groups. 1. Introduction. Let fj: G! PSL2(C)g be a sequence of discrete, faith-ful representations of a finitely generated, torsion-free, nonabelian group G which converges to a representation : G! PSL2(C). By passing to a subsequence, we may assume that fj(G)g converges, as a sequence of closed subsets of PSL2(C), to a torsion-free, nonabelian Kleinian group bΓ with (G) bΓ. We call (G) th