Representations of virtual braids by automorphisms and virtual knot groups

2016/03/04 by Bardakov, V. G., Mikhalchishina, Yu. A., Neshchadim, M. V.
#Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1603.01425

Abstract

In the present paper the representation of the virtual braid group VB_n 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 these already known representations are not faithful for n ≥ 4 is verified. Using representations of VB_n, the virtual link group is defined. Also representations of welded braid group WB_n are constructed and the welded link group is defined.

Related

• Representations of flat virtual braids by automorphisms of free group
• Representations of flat virtual braids which do not preserve the forbidden relations
• The virtual and universal braids
• Virtual Braids
• Unrestricted virtual braids, fused links and other quotients of virtual braid groups