#### Volume 7, issue 3 (2007)

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High distance knots

### Yair N Minsky, Yoav Moriah and Saul Schleimer

Algebraic & Geometric Topology 7 (2007) 1471–1483
 arXiv: math.GT/0607265
##### 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 $\left(t,b\right)$–decomposition.

##### Keywords
Heegaard distance, tunnel number, knot, bridge position
##### Mathematical Subject Classification 2000
Primary: 57M25, 57M27