  By exploring simplicial structure of pure virtual braid groups, we give new
connections between the homotopy groups of the 3-sphere and the virtual braid
groups that are related to the theory of Brunnian virtual braids. The group
structure of VP_n with n > 4 is determined by VP_3, VP_4 and virtual cablings
given by iterated degeneracy operations on the generators and defining
relations. The complete proofs will be published in the two forthcoming papers.
