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)} ≤ 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.