VIRTUAL BRAIDS AND THE L-MOVE

Abstract

In this paper we prove a Markov theorem for virtual braids and for analogs of this structure including flat virtual braids and welded braids. 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 this paper we follow L-move methods to prove the Virtual Markov theorems. One benefit of this approach is a fully local algebraic formulation of the theorems in each category.