The visual core of a hyperbolic 3-manifold

Abstract

We introduce the notion of the visual core of a hyperbolic 3-manifold N and explore its basic properties. The visual core can be thought of as a harmonic analysis analogue of the convex core. We investigate circumstances in which the visual core of a cover N' of N embeds under the covering map from N' to N. We apply this analysis to convergent sequences of Kleinian groups, in order to understand when the visual core of the algebraic limit manifold embeds in the geometric limit manifold. We close with a discussion of the behavior of the visual core under Klein-Maskit combination.