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 virtual braid group is an extension of the classical braid group by the symmetric group. In [13] a Markov Theorem is proved for virtual braids, giving a set of moves on virtual braids that generate the same equivalence classes as the virtual link types of their closures. Such theorems are important for understanding the structure and classification of virtual knots and links.