The visual core of a hyperbolic 3-manifold

Abstract

In this note we introduce the notion of the visual core of a hyperbolic 3-manifold \(N={\bf H}^3/\Gamma\), and explore some of its basic properties. We investigate circumstances under which the visual core \({\cal V}(N')\) of a cover \(N'={\bf H}^3/\Gamma'\) of N embeds in N, via the usual covering map \(\pi: N'\rightarrow N\). We go on to show that if the algebraic limit of a sequence of isomorphic Kleinian groups is a generalized web group, then the visual core of the algebraic limit manifold embeds in the geometric limit manifold. Finally, we discuss the relationship between the visual core and Klein-Maskit combination along component subgroups.