Algebraic & Geometric Topology

High distance knots

Yair N Minsky, Yoav Moriah, and Saul Schleimer

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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.

Article information

Algebr. Geom. Topol., Volume 7, Number 3 (2007), 1471-1483.

Received: 25 August 2006
Accepted: 22 March 2007
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds

Heegaard distance tunnel number knot bridge position


Minsky, Yair N; Moriah, Yoav; Schleimer, Saul. High distance knots. Algebr. Geom. Topol. 7 (2007), no. 3, 1471--1483. doi:10.2140/agt.2007.7.1471.

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