Groups of virtual and welded links

Abstract

We define a new notion of group of virtual and welded links. We use two approaches for defining it: via representations of (generalized) braids by automorphisms of free groups and via Wirtinger-like labeling on virtual and welded diagrams. In the case of virtual links our invariant is stronger than the notion of fundamental group of a virtual link introduced by Kauffman. In the case of welded links our invariant coincides with Kauffman invariant, but using a generalization of Wada representations we provide new families of invariants of welded links.