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

作者：Kadokami, Teruhisa^*; Kawamura, Kengo

来源：Journal of Knot Theory and Its Ramifications, 2014, 23(13): 1450071.

DOI：10.1142/S0218216514500710

• Clasp disk
• clasp number
• Conway polynomial
• Jones polynomial

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)} <= 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.

• 出版日期2014-11
• 单位华东师范大学