On Vassiliev Invariants of Virtual Knots
arXiv:2208.10467
Abstract
We discuss Vassiliev invariants for virtual knots, expanding upon the theory of quantum virtual knot invariants developed in arXiv:1509.00578. In particular, following the theory of quantum invariants we work with 'rotational' virtual knots. We define chord diagrams, weight systems, and give examples of Lie algebra weight systems of rotational virtual knots. We end with a discussion of extended quantum invariants, which capture information that standard quantum invariants of rotational virtuals cannot.
33 pages, 36 figures, Material from Section 4 of version 1 has been deferred pending further research