High distance knots

Yair N Minsky; Yoav Moriah; Saul Schleimer

doi:10.2140/agt.2007.7.1471

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Home > Journals > Algebr. Geom. Topol. > Volume 7 > Issue 3 > Article

2007 High distance knots

Yair N Minsky, Yoav Moriah, Saul Schleimer

Algebr. Geom. Topol. 7(3): 1471-1483 (2007). DOI: 10.2140/agt.2007.7.1471

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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 $(t, b)$ –decomposition.

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Yair N Minsky. Yoav Moriah. Saul Schleimer. "High distance knots." Algebr. Geom. Topol. 7 (3) 1471 - 1483, 2007. https://doi.org/10.2140/agt.2007.7.1471