An infinite family of prime knots with a certain property for the clasp number

Teruhisa Kadokami; Kengo Kawamura

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arXiv · 1405.0143

An infinite family of prime knots with a certain property for the clasp number

Teruhisa Kadokami·Kengo Kawamura

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Abstract

The clasp number $c(K)$ of a knot $K$ is the minimum number of clasp singularities among all clasp disks bounded by $K$. It is known that the genus $g(K)$ and the unknotting number $u(K)$ are lower bounds of the clasp number, that is, $\max\{g(K),u(K)\} \leq c(K)$. Then it is natural to ask whether there exists a knot $K$ such that $\max\{g(K),u(K)\}<c(K)$. In this paper, we prove that there exists an infinite family of prime knots such that the question above is affirmative.

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BibTeX RIS

Teruhisa Kadokami, Kengo Kawamura. 2014-10-15. An infinite family of prime knots with a certain property for the clasp number. https://arxiv.org/abs/1405.0143

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