Polyak type equations for virtual arrow diagram formulas in the annulus

Abstract

We describe the space of arrow diagram formulas for virtual knot diagrams in the annulus as the kernel of a linear map, inspired from a conjecture due to M. Polyak. As a main application, we slightly improve Grishanov-Vassiliev's theorem for planar chain invariants.

arXiv comment21 pages, 15 figures

Cited by in corpus (3)

• On Usual, Virtual and Welded knotted objects up to homotopy
• Combinatorial cohomology of the space of long knots
• Finite-type 1-cocycles of knots given by Polyak-Viro formulas