English

On Vassiliev Invariants of Virtual Knots

Geometric Topology 2022-09-20 v2 Quantum Algebra

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.

Keywords

Cite

@article{arxiv.2208.10467,
  title  = {On Vassiliev Invariants of Virtual Knots},
  author = {Wout Moltmaker and Louis H. Kauffman},
  journal= {arXiv preprint arXiv:2208.10467},
  year   = {2022}
}

Comments

33 pages, 36 figures, Material from Section 4 of version 1 has been deferred pending further research