Exceptional and cosmetic surgeries on knots
Geometric Topology
2016-01-06 v3
Abstract
We show that the distance of a link with respect to a bridge surface of any genus determines a lower bound on the genus of essential surfaces and Heegaard surfaces in the manifolds that result from non-trivial Dehn surgeries on the knot. In particular, knots with high bridge distance do not admit non-trivial non-hyperbolic surgeries or non-trivial cosmetic surgeries. We further show that if a knot has bridge distance at least 3 then its bridge number is bounded above by a function of Seifert genus, or indeed by the genus of (almost) any essential surface or Heegaard surface in the surgered manifold.
Keywords
Cite
@article{arxiv.1209.0197,
title = {Exceptional and cosmetic surgeries on knots},
author = {Ryan Blair and Marion Campisi and Jesse Johnson and Scott A. Taylor and Maggy Tomova},
journal= {arXiv preprint arXiv:1209.0197},
year = {2016}
}
Comments
The new version strengthens the results, incorporates arXiv:1211.4787 and incorporates referee comments. 50 pages, 8 figures