Unknotting numbers of diagrams of a given nontrivial knot are unbounded

Kouki Taniyama

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arXiv · 0805.3174

Unknotting numbers of diagrams of a given nontrivial knot are unbounded

Kouki Taniyama

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Abstract

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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BibTeX RIS

Kouki Taniyama. 2008-06-22. Unknotting numbers of diagrams of a given nontrivial knot are unbounded. https://arxiv.org/abs/0805.3174

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