A polynomial invariant of virtual knots

Abstract

The aim of this paper is to introduce a polynomial invariant $f_K(t)$ for virtual knots. We show that $f_K(t)$ can be used to distinguish some virtual knot from its inverse and mirror image. The behavior of $f_K(t)$ under connected sum is also given. Finally we discuss which kind of polynomial can be realized as $f_K(t)$ for some virtual knot $K$.

11 pages, 16 figures