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

Arnaud Mortier (1)

1 OCAMI - Osaka City university Advanced Mathematical Institute [Osaka]

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.

Mots clés: 1-cocycles; Vassiliev invariants; finite-type; Teiblum-Turchin; Polyak-Viro

Domaines: Topologie géométrique [math.GT]

Arnaud Mortier. Finite-type 1-cocycles of knots given by Polyak-Viro formulas. 2014. ⟨hal-00958618⟩