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An infinite family of prime knots with a certain property for the clasp number
- Publication Year :
- 2014
-
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.<br />Comment: 13 pages, 12 figures
- Subjects :
- Mathematics - Geometric Topology
57M25 57M27
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1405.0143
- Document Type :
- Working Paper