On the arc index of Kanenobu knots

Abstract

In this paper, we calculate the Kauffman polynomials [Formula: see text] of Kanenobu knots [Formula: see text] with [Formula: see text] half twists and determine their spans on the variable [Formula: see text] 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: see text] by using canonical cabling algorithm and the 2-cable [Formula: see text]-polynomials. Moreover, we give sharper upper bounds of the arc index of some Kanenobu knots by using their braid presentations.