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

arXiv eprints
 Pub Date:
 May 2014
 arXiv:
 arXiv:1405.0143
 Bibcode:
 2014arXiv1405.0143K
 Keywords:

 Mathematics  Geometric Topology;
 57M25 57M27
 EPrint:
 13 pages, 12 figures