English

The Wriggle polynomial for virtual tangles

Geometric Topology 2019-04-24 v1

Abstract

We generalize the Wriggle polynomial, first introduced by L. Folwaczny and L. Kauffman, to the case of virtual tangles. This generalization naturally arises when considering the self-crossings of the tangle. We prove that the generalization (and, by corollary, the original polynomial) are Vassiliev invariants of order one for virtual knots, and study some simple properties related to the connected sum of tangles.

Keywords

Cite

@article{arxiv.1904.10299,
  title  = {The Wriggle polynomial for virtual tangles},
  author = {Nicolas Petit},
  journal= {arXiv preprint arXiv:1904.10299},
  year   = {2019}
}

Comments

14 pages, 17 figures. arXiv admin note: text overlap with arXiv:1805.08178

R2 v1 2026-06-23T08:47:12.783Z