Unknotting numbers of diagrams of a given nontrivial knot are unbounded

Details Unknotting numbers of diagrams of a given nontrivial knot are unbounded Unknotting numbers of diagrams of a given nontrivial knot are unbounded

2008-05-20

arxiv.org/abs/0805.3174v2

Mathematics

Geometric Topology

13 pages, 14 figures. Theorem 1.4 and Theorem 1.5 added

Scientific paper

We show that for any nontrivial knot $K$ and any natural number $n$ there is
a diagram $D$ of $K$ such that the unknotting number of $D$ is greater than or
equal to $n$. It is well known that twice the unknotting number of $K$ is less
than or equal to the crossing number of $K$ minus one. We show that the
equality holds only when $K$ is a $(2,p)$-torus knot.

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