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

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

2006-06-09

arxiv.org/abs/math/0606226v3

Mathematics

Geometric Topology

7 pages

Scientific paper

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
$(1,n)$.

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