%0 Journal Article
%T On tunnel number one knots that are not (1,n)
%A Jesse Johnson
%A Abigail Thompson
%J Mathematics
%D 2006
%I arXiv
%X 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 $(1,n)$.
%U http://arxiv.org/abs/math/0606226v3