Dynnikov coordinates on virtual braid groups

Valerij G. Bardakov (1) , Andrei Vesnin (1) , Bert Wiest (2)

1 Sobolev Institute of Mathematics
2 IRMAR - Institut de Recherche Mathématique de Rennes

We define Dynnikov coordinates on virtual braid groups. We prove that they are faithful invariants of virtual 2-braids, and present evidence that they are also very powerful invariants for general virtual braids.

Mots clés: Braid; virtual braid; Dynnikov coordinates; faithful invariants

Domaines: Topologie géométrique [math.GT]; Théorie des groupes [math.GR]

Valerij G. Bardakov, Andrei Vesnin, Bert Wiest. Dynnikov coordinates on virtual braid groups. Journal of Knot Theory and Its Ramifications, 2012, 21 (5), ⟨10.1142/S021821651101005X⟩. ⟨hal-00577935v2⟩