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

• Main Authors: Kadokami, Teruhisa, Kawamura, Kengo
• Format: Journal Article
• Language: English
• Published: 01-05-2014
• Subjects: Mathematics - Geometric Topology
• DOI: 10.48550/arxiv.1405.0143

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.