A refinement of the first Vassiliev invariant can distinguish the orientation of knots

Thomas Fiedler

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arXiv · 1902.06091

A refinement of the first Vassiliev invariant can distinguish the orientation of knots

Thomas Fiedler

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Abstract

We refine the Polyak-Viro Gauss diagram formula for the Vassiliev invariant of order two in a very simple way for the 2-cable of a framed long knot. Surprisingly, the resulting isotopy invariant of framed knots can detect already the non-invertibility of knots. This makes the natural generalization of our invariant for all n-component string link satellites of a framed long knot to a candidate for distinguishing all classical knots.

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Thomas Fiedler. 2019-02-16. A refinement of the first Vassiliev invariant can distinguish the orientation of knots. https://arxiv.org/abs/1902.06091

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