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

@article{Kadokami2014AnIF, title={An infinite family of prime knots with a certain property for the clasp number}, author={Teruhisa Kadokami and Kengo Kawamura}, journal={arXiv: Geometric Topology}, year={2014} }

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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