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 S3 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
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