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
$(1,n)$.Comment: 7 page

Johnson, Jesse

Thompson, Abigail

English

arXiv

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 $(1,n)$

On tunnel number one knots that are not (1,n)

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