A simple solution to the word problem for virtual braid groups
We show a simple and easily implementable solution to the word problem for virtual braid groups.
math.GR↗
arXiv subjects
Bruno Aaron Cisneros de La Cruz
Publications and source records attributed to Bruno Aaron Cisneros de La Cruz.
Virtual braids from a topological viewpoint
Virtual braids are a combinatorial generalization of braids. We present abstract braids as equivalence classes of braid diagrams on a surface, joining two distinguished boundary components. They are identified up to isotopy, compatibility, stability and Reidemeister moves. We show that virtual braids are in a bijective correspondence with abstract braids. Finally we demonstrate that for any abstract braid, its representative of minimal genus is unique up to compatibility and Reidemeister moves. The genus of such a representative is thus an invariant for virtual braids. We also give a complete proof of the fact that there is a bijective correspondence between virtually equivalent virtual braid diagrams and braid-Gauss diagrams.
math.GR↗