High distance knots

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.

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Keywords

Heegaard distance, tunnel number, knot, bridge position

Mathematical Subject Classification 2000

Primary: 57M25, 57M27

References

Publication

Received: 25 August 2006

Accepted: 22 March 2007

Published: 14 November 2007

Authors

Yair N Minsky
Department of Mathematics Yale University New Haven CT 06520-8283 USA

Yoav Moriah
Department of Mathematics Technion Haifa 32000 Israel

Saul Schleimer
Mathematics Institute University of Warwick Coventry CV4 7AL UK

Volume 7, issue 3 (2007)

Yair N Minsky, Yoav Moriah and Saul Schleimer

Abstract