### Abstract

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

Original language | English |
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Pages (from-to) | 87-100 |

Number of pages | 14 |

Journal | Topology and its Applications |

Volume | 184 |

DOIs | |

Publication status | Published - 2015 Apr 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Clasper
- HOMFLYPT polynomial
- Milnor μ--invariant

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

**Milnor invariants of length 2k+2 for links with vanishing Milnor invariants of length ≤k.** / Kotorii, Yuka; Yasuhara, Akira.

Research output: Contribution to journal › Article

*Topology and its Applications*, vol. 184, pp. 87-100. https://doi.org/10.1016/j.topol.2015.01.003

}

TY - JOUR

T1 - Milnor invariants of length 2k+2 for links with vanishing Milnor invariants of length ≤k

AU - Kotorii, Yuka

AU - Yasuhara, Akira

PY - 2015/4/1

Y1 - 2015/4/1

N2 - J.-B. Meilhan and the second author showed that any Milnor μ--invariant of length between 3 and 2. k+. 1 can be represented as a combination of HOMFLYPT polynomial of knots obtained by certain band sum of the link components, if all μ--invariants of length ≤. k vanish. They also showed that their formula does not hold for length 2. k+. 2. In this paper, we improve their formula to give the μ--invariants of length 2. k+. 2 by adding correction terms. The correction terms can be given by a combination of HOMFLYPT polynomial of knots determined by μ--invariants of length k+. 1. In particular, for any 4-component link the μ--invariants of length 4 are given by our formula, since all μ--invariants of length 1 vanish.

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

KW - Clasper

KW - HOMFLYPT polynomial

KW - Milnor μ--invariant

UR - http://www.scopus.com/inward/record.url?scp=84922989840&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84922989840&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2015.01.003

DO - 10.1016/j.topol.2015.01.003

M3 - Article

AN - SCOPUS:84922989840

VL - 184

SP - 87

EP - 100

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

ER -