On tunnel number one knots that are not (1,n)
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 $(1,n)$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606226
 Bibcode:
 2006math......6226J
 Keywords:

 Mathematics  Geometric Topology;
 57M
 EPrint:
 7 pages