A multivariable polynomial invariant of virtual links and cut systems

Abstract

The notion of cut points on a virtual link diagram was introduced by H. A. Dye and it was extended by the author to the notion of oriented cut points. Using oriented cut points, one can often apply some arguments working only on almost classical virtual link diagrams to any virtual link diagram. In this paper we construct a multivariable polynomial XD for a virtual link diagram using oriented cut points. It turns out that this polynomial is the same with the multivariable polynomial invariant of virtual links introduced by H. A. Dye and L. H. Kauffman and by Y. Miyazawa independently. Using this fact, we give some properties of the multivariable polynomial invariant and some applications.