Wild Knots as limit sets of Kleinian Groups

Details Wild Knots as limit sets of Kleinian Groups Wild Knots as limit sets of Kleinian Groups

2005-09-06

arxiv.org/abs/math/0509124v1

Mathematics

Geometric Topology

20 pages, 6 figures. To appear in Contemporary Mathematics

Scientific paper

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.

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