English

Wild Knots as limit sets of Kleinian Groups

Geometric Topology 2007-05-23 v1

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 Λ\Lambda also fibers over the circle. As a consequence, the universal covering of S3Λ\mathbb{S}^{3}-\Lambda is R3\mathbb{R}^{3}. We prove that the complement of a dynamically-defined fibered wild knot can not be a complete hyperbolic 3-manifold.

Cite

@article{arxiv.math/0509124,
  title  = {Wild Knots as limit sets of Kleinian Groups},
  author = {Gabriela Hinojosa},
  journal= {arXiv preprint arXiv:math/0509124},
  year   = {2007}
}

Comments

20 pages, 6 figures. To appear in Contemporary Mathematics

R2 v1 2026-07-22T17:24:12.530Z