Vassiliev knot invariants derived from cable Γ-polynomials

Abstract

For coprime integers p(>0) and q, the (p,q)-cable Γ-polynomial of a knot K is the Γ-polynomial of the (p,q)-cable knot of K, where the Γ-polynomial is the common zeroth coefficient polynomial of the HOMFLYPT and Kauffman polynomials. In this paper, we give some results on Vassiliev knot invariants derived from the cable Γ-polynomials. In particular, we show that all Vassiliev knot invariants of order ≤4 are determined by the cable Γ-polynomials.