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

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.

24 pages, 23 images

References in corpus (3)

• Knot polynomials via one parameter knot theory
• Quantum one-cocycles for knots
• Virtual knot theory on a group

Cited by in corpus (3)

• Combinatorial cohomology of the space of long knots
• Singularization of knots and closed braids
• A Kontsevich integral of order 1