The limit set intersection theorem for finitely generated Kleinian groups

The proof of the Theorem proceeds by showing that it holds in some special cases involving Kleinian groups with connected limit sets, and then extending to the general case by using a decomposition argument based on the Klein-Maskit combination theorems and a careful tracking of the limit points resulting from this decomposition. We discuss various well-behaved classes of limit points in Section 2. We describe the decomposition results taken from Klein-Maskit combination theory in Section 3. We apply the decomposition results to a special subclass of groups in Section 4. We then complete the proof in Section 5. In Section 6, we discuss the extension of Theorem 5.4 to groups with torsion, the difficulty with extending to groups with parabolics, and make note of a reduction of the Ahlfors measure conjecture.