Goussarov-Habiro theory for string links and the Milnor-Johnson correspondence |
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Authors: | Jean-Baptiste Meilhan |
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Institution: | Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa, Sakyo-ku, Kyoto 606-8502, Japan |
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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 μ invariant. These invariants are seen to be naturally related to invariants of homology cylinders through the 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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Keywords: | Finite type invariant String link Homology cylinder Clasper |
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