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We construct a universal Vassiliev invariant for braid groups of the sphereand the mapping class groups of the sphere with $n$ punctures. The case of asphere is different from the classical braid groups or braids of orientedsurfaces of genus strictly greater than zero, since Vassiliev invariants in agroup without 2-torsion do not distinguish elements of braid group of a sphere.

On Vassiliev invariants of braid groups of the sphere