Milnor invariants of length $2k+2$ for links with vanishing Milnor invariants of length $\leq k$

Yuka Kotorii; Akira Yasuhara

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arXiv · 1304.1870

Milnor invariants of length $2k+2$ for links with vanishing Milnor invariants of length $\leq k$

Yuka Kotorii·Akira Yasuhara

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Abstract

J.-B. Meilhan and the second author showed that any Milnor $\barμ$-invariant of length between 3 and $2k+1$ can be represented as a combination of HOMFLYPT polynomial of knots obtained by certain band sum of the link components, if all $\barμ$-invariants of length $\leq k$ vanish. They also showed that their formula does not hold for length $2k+2$. In this paper, we improve their formula to give the $\barμ$-invariants of length $2k+2$ by adding correction terms. The correction terms can be given by a combination of HOMFLYPT polynomial of knots determined by $\barμ$-invariants of length $k+1$. In particular, for any 4-component link the $\barμ$-invariants of length 4 are given by our formula, since all $\barμ$-invariants of length 1 vanish.

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BibTeX RIS

Yuka Kotorii, Akira Yasuhara. 2013-04-06. Milnor invariants of length $2k+2$ for links with vanishing Milnor invariants of length $\leq k$. https://arxiv.org/abs/1304.1870

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