Goussarov-Habiro theory for string links and the Milnor-Johnson   correspondence
  We study the Goussarov-Habiro finite type invariants theory for framed string links in homology balls.   Their degree 1 invariants are computed: they are given by Milnor's triple linking numbers, the mod 2 reduction of the Sato-Levine invariant, Arf and Rochlin's $\mu$ invariant. These invariants are seen to be naturally related to invariants of homology cylinders through the so-called Milnor-Johnson correspondence: in particular, an analogue of the Birman-Craggs homomorphism for string links is computed.   The relation with Vassiliev theory is studied. 
Jean-Baptiste Meilhan