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arXiv · 1002.1803

Milnor invariants and the HOMFLYPT polynomial

Jean-Baptiste Meilhan·Akira Yasuhara
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Abstract

We give formulas expressing Milnor invariants of an n-component link L in the 3-sphere in terms of the HOMFLYPT polynomial as follows. If the Milnor invariant \barμ_J(L) vanishes for any sequence J with length at most k, then any Milnor \barμ-invariant \barμ_I(L) with length between 3 and 2k+1 can be represented as a combination of HOMFLYPT polynomial of knots obtained from the link by certain band sum operations. In particular, the `first non vanishing' Milnor invariants can be always represented as such a linear combination.

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Jean-Baptiste Meilhan, Akira Yasuhara. 2011-06-06. Milnor invariants and the HOMFLYPT polynomial. https://doi.org/10.2140/gt.2012.16.889

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