ABSTRACT

We have already considered some generalisations of basic knot invariants: the colouring invariant, the fundamental group and the Jones-Kauffman polynomial [KaVi].

All the generalisations described above were constructed by using the following idea: one thinks of a virtual link diagram as a set of classical crossings provided with the information about how they are connected on the plane and one does not pay attention to virtual crossings. Thus, for instance, the generators of the fundamental group that correspond to arcs of the diagram may pass through virtual crossings, and all relations are taken only at classical crossings.