### 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 |

### Keywords

- Clasper
- HOMFLYPT polynomial
- Milnor μ--invariant

### ASJC Scopus subject areas

- Geometry and Topology