Milnor invariants and the HOMFLYPT polynomial

Jean Baptiste Meilhan*, Akira Yasuhara

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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 ̄μL(J) vanishes for any sequence J with length at most k, then any Milnor ̄μ-invariant ̄μL(I) 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 nonvanishing Milnor invariants can be always represented as such a linear combination.

Original languageEnglish
Pages (from-to)889-917
Number of pages29
JournalGeometry and Topology
Issue number2
Publication statusPublished - 2012
Externally publishedYes

ASJC Scopus subject areas

  • Geometry and Topology


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