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High distance knots

Yair Minsky·Yoav Moriah·Saul Schleimer
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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 Minsky, Yoav Moriah, Saul Schleimer. 2007-08-15. High distance knots. https://doi.org/10.2140/agt.2007.7.1471

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