Goussarov-Habiro theory for string links and the Milnor-Johnson correspondence
arXiv:math/0402035
Abstract
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 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.
arXiv comment23 pages. New exposition. One new section (relation with Vassiliev theory). To appear in Topology & its Applications