A Sequence of Degree One Vassiliev Invariants for Virtual Knots
By Allison Henrich. 2008
93 citations recorded by the source corpus.
For ordinary knots in R3, there are no degree one Vassiliev invariants. For virtual knots, however, the space of degree one Vassiliev invariants is infinite dimensional. We introduce a sequence of three degree one Vassiliev invariants of virtual knots of increasing strength. We demonstrate that the strongest invariant is a universal Vassiliev invariant of degree one for virtual knots in the sense that any other degree one Vassiliev invariant can be recovered from it by a certain natural construction. To prove these results, we extend the based matrix invariant introduced by Turaev for virtual strings to the class of singular virtual knots with one double-point.
View Paper: https://www.semanticscholar.org/paper/ef2b8c29cea0c165cd217fa44e3f57dd60ad4732
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Citations in the corpus
- A polynomial invariant of virtual links (2013, methodology): “The main idea of the odd writhe polynomial is assigning a weight to each crossing, the similar idea was used by A. Henrich to define three kinds of degree one Vassiliev invariants in [5].”
- An Affine Index Polynomial Invariant of Virtual Knots (2012, background): “Henrich [11] to a new polynomial invariant of virtual knots and links.”