On the arc index of Kanenobu knots

Abstract

In this paper, we calculate the Kauffman polynomials (Formula presented.) of Kanenobu knots (Formula presented.) with (Formula presented.) half twists and determine their spans on the variable (Formula presented.) completely. As an application, we determine the arc index of infinitely many Kanenobu knots. In particular, we give sharper lower bounds of the arc index of (Formula presented.) by using canonical cabling algorithm and the 2-cable (Formula presented.)-polynomials. Moreover, we give sharper upper bounds of the arc index of some Kanenobu knots by using their braid presentations. ? 2017 World Scientific Publishing Company