Wild Knots as limit sets of Kleinian Groups

Abstract

In this paper we study kleinian groups of Schottky type whose limit set is a wild knot in the sense of Artin and Fox. We show that, if the ``original knot'' fibers over the circle then the wild knot $\Lambda$ also fibers over the circle. As a consequence, the universal covering of ${\mathbb{S}}^3-\Lambda$ is ${\mathbb{R}}^3$. We prove that the complement of a dynamically-defined fibered wild knot can not be a complete hyperbolic 3-manifold.

20 pages, 6 figures. To appear in Contemporary Mathematics