High distance knots
Geometric Topology
2014-10-01 v3
Abstract
We construct knots in S^3 with Heegaard splittings of arbitrarily high distance, in any genus. As an application, for any positive integers t and b we find a tunnel number t knot in the three-sphere which has no (t,b)-decomposition.
Keywords
Cite
@article{arxiv.math/0607265,
title = {High distance knots},
author = {Yair Minsky and Yoav Moriah and Saul Schleimer},
journal= {arXiv preprint arXiv:math/0607265},
year = {2014}
}
Comments
13 pages, 3 figures. Added reference