Goussarov-Habiro theory for string links and the Milnor-Johnson correspondence

Details Goussarov-Habiro theory for string links and the Milnor-Johnson correspondence Goussarov-Habiro theory for string links and the Milnor-Johnson correspondence

2004-02-03

arxiv.org/abs/math/0402035v2

Topology Appl. 153 (2006), No. 14, 2709-2729

Mathematics

Geometric Topology

23 pages. New exposition. One new section (relation with Vassiliev theory). To appear in Topology & its Applications

Scientific paper

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.

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