High distance knots

By Yair N. Minsky, Y. Moriah, Saul Schleimer. 2006

47 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/086a30578a5ec033d18c5764b7969169c3a4519d