### 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 ̄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 language | English |
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Pages (from-to) | 889-917 |

Number of pages | 29 |

Journal | Geometry and Topology |

Volume | 16 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2012 Jul 9 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Geometry and Topology*,

*16*(2), 889-917. https://doi.org/10.2140/gt.2012.16.889

**Milnor invariants and the HOMFLYPT polynomial.** / Meilhan, Jean Baptiste; Yasuhara, Akira.

Research output: Contribution to journal › Article

*Geometry and Topology*, vol. 16, no. 2, pp. 889-917. https://doi.org/10.2140/gt.2012.16.889

}

TY - JOUR

T1 - Milnor invariants and the HOMFLYPT polynomial

AU - Meilhan, Jean Baptiste

AU - Yasuhara, Akira

PY - 2012/7/9

Y1 - 2012/7/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84863458597&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863458597&partnerID=8YFLogxK

U2 - 10.2140/gt.2012.16.889

DO - 10.2140/gt.2012.16.889

M3 - Article

VL - 16

SP - 889

EP - 917

JO - Geometry and Topology

JF - Geometry and Topology

SN - 1465-3060

IS - 2

ER -