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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 $μ$ 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.

preprint2005arXivOpen access
Jean-Baptiste Meilhan
math.GT
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Jean-Baptiste Meilhan

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