Links with no exceptional surgeries
Geometric Topology
2014-05-20 v3
Abstract
We show that if a knot admits a prime, twist-reduced diagram with at least 4 twist regions and at least 6 crossings per twist region, then every non-trivial Dehn filling of that knot is hyperbolike. A similar statement holds for links. We prove this using two arguments, one geometric and one combinatorial. The combinatorial argument further implies that every link with at least 2 twist regions and at least 6 crossings per twist region is hyperbolic and gives a lower bound for the genus of a link.
Keywords
Cite
@article{arxiv.math/0412307,
title = {Links with no exceptional surgeries},
author = {David Futer and Jessica S. Purcell},
journal= {arXiv preprint arXiv:math/0412307},
year = {2014}
}
Comments
28 pages, 15 figures. Minor rewording and organizational changes; also added theorem giving a lower bound on the genus of these links