A Sequence of Degree One Vassiliev Invariants for Virtual Knots

Allison Henrich

doi:10.1142/10.1142/s0218216510007917

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arXiv · 0803.0754

A Sequence of Degree One Vassiliev Invariants for Virtual Knots

Allison Henrich

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Abstract

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.

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Allison Henrich. 2008-04-03. A Sequence of Degree One Vassiliev Invariants for Virtual Knots. https://doi.org/10.1142/10.1142%2Fs0218216510007917

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