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

2019/02/16 by Fiedler, Thomas
#57M25 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1902.06091

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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