On Vassiliev invariants of braid groups of the sphere
  We construct a universal Vassiliev invariant for braid groups of the sphere and the mapping class groups of the sphere with $n$ punctures. The case of a sphere is different from the classical braid groups or braids of oriented surfaces of genus strictly greater than zero, since Vassiliev invariants in a group without 2-torsion do not distinguish elements of braid group of a sphere. 
N. Kaabi and V. V. Vershinin
math.GR