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 algebraic 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.