Virtual Braids and the L–Move

The L–Move and Virtual Braids

5 Virtual Braids and the L – Move

In this paper we prove a Markov Theorem for the virtual braid group and for some analogs of this structure. The virtual braid group is the natural companion to the category of virtual knots, just as the Artin braid group is the natural companion to classical knots and links. In classical knot theory the braid group gives a fundamental algebraic structure associated with knots. The Alexander The...

2 00 4 Virtual Braids

Just as classical knots and links can be represented by the closures of braids, so can virtual knots and links be represented by the closures of virtual braids [17]. Virtual braids have a group structure that can be described by generators and relations, generalizing the generators and relations of the classical braid group. This structure of virtual braids is worth study for its own sake. The ...

Virtual Braids

Just as classical knots and links can be represented by the closures of braids, so can virtual knots and links be represented by the closures of virtual braids [16]. Virtual braids have a group structure that can be described by generators and relations, generalizing the generators and relations of the classical braid group. This structure of virtual braids is worth study for its own sake. The ...

Dynnikov coordinates on virtual braid groups

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.