English

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