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arXiv · 1403.3418

Finite-type 1-cocycles of knots given by Polyak-Viro formulas

Arnaud Mortier
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Abstract

We present a new method to produce simple formulas for 1-cocycles of knots over the integers, inspired by Polyak-Viro's formulas for finite-type knot invariants. We conjecture that these formulas always represent finite-type cohomology classes in the sense of Vassiliev. An example of degree 3 is studied, and shown to coincide over Z/2 with the Teiblum-Turchin cocycle v_3^1.

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Arnaud Mortier. 2014-03-13. Finite-type 1-cocycles of knots given by Polyak-Viro formulas. https://doi.org/10.1142/s0218216515400040

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