High distance knots
Yair Minsky, Yoav Moriah, Saul Schleimer
math.GTarXiv:math/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.
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