A two-variable polynomial invariant of virtual knots

Abstract

In this paper, we introduce a polynomial invariant of virtual knots by using weights of crossings. It is motivated from the writhe polynomial and the affine index polynomial for virtual knots. The new polynomial invariant is distinct from these polynomials and is a Vassiliev invariant of degree 1. By using the polynomial invariant we give a lower bound for the Gordian distance of two homotopic virtual knots.