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On tunnel number one knots that are not (1,n)
Published Web Location
https://arxiv.org/pdf/math/0606226.pdfNo data is associated with this publication.
Abstract
We show that the bridge number of a $t$ bridge knot in $S^3$ with respect to an unknotted genus $t$ surface is bounded below by a function of the distance of the Heegaard splitting induced by the $t$ bridges. It follows that for any natural number $n$, there is a tunnel number one knot in $S^3$ that is not $(1,n)$.