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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- September 2005
- DOI:
- arXiv:
- arXiv:math/0509124
- Bibcode:
- 2005math......9124H
- Keywords:
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- Geometric Topology;
- 57M30;
- 57M45;
- 57Q45;
- 30F14
- E-Print:
- 20 pages, 6 figures. To appear in Contemporary Mathematics