Geometric decomposition of spatial Kleinian groups and fundamental groups of 3-manifolds (Q910767)

Let G be a finitely generated group of Möbius transformations of the 3- dimensional Möbius space \({\mathbb{R}}^ 3\cup \{\infty \}\). Suppose that G is a functional Kleinian group and that G acts freely on an invariant component \(\Omega\). Let \(M=\Omega /G\). Suppose further that G is isomorphic to the fundamental group of a Haken manifold with toroidal boundary. Under these assumptions the author proves that every decomposition \(G=G_ 1*_{G_ 2}G_ 3\) or \(G=G_ 1*_{G_ 2}\) can be realized by an incompressible surface in M. This extends some work of Maskit.