Representations of virtual braids by automorphisms and virtual knot groups

Abstract

In the present paper, a new representation of the virtual braid group [Formula: see text] into the automorphism group of free product of the free group and free abelian group is constructed. This representation generalizes the previously constructed ones. The fact that the previously known representations are not faithful for [Formula: see text] is verified. Using representations of [Formula: see text], a virtual link group is defined. Also representations of the welded braid group [Formula: see text] are constructed and the welded link group is defined.