2019/04/19 by Nicolas Petit, Petit, Nicolas
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT
paper · pdf · doi:10.48550/arxiv.1904.10299
14 pages, 17 figures. arXiv admin note: text overlap with arXiv:1805.08178
arxiv created 2019/04/19 · arxiv updated 2019/04/24
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.