Polyak type equations for virtual arrow diagram formulas in the annulus

Arnaud Mortier (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: virtual; Gauss; arrow; Vassiliev; diagram; Polyak

Domaines: Topologie géométrique [math.GT]

Arnaud Mortier. Polyak type equations for virtual arrow diagram formulas in the annulus. Journal of Knot Theory and Its Ramifications, 2013, vol. 22 (7), pp.1350034, 21. ⟨10.1142/S021821651350034X⟩. ⟨hal-00737684v2⟩