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.