Milnor invariants and the HOMFLYPT polynomial

Jean Baptiste Meilhan, Akira Yasuhara

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)889-917
Number of pages29
JournalGeometry and Topology
Volume16
Issue number2
DOIs
Publication statusPublished - 2012 Jul 9
Externally publishedYes

Fingerprint

Polynomial
Invariant
Knot
Linear Combination
Vanish

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

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

In: Geometry and Topology, Vol. 16, No. 2, 09.07.2012, p. 889-917.

Research output: Contribution to journalArticle

Meilhan, Jean Baptiste ; Yasuhara, Akira. / Milnor invariants and the HOMFLYPT polynomial. In: Geometry and Topology. 2012 ; Vol. 16, No. 2. pp. 889-917.
@article{45db684b3fe8440e9df1040268a2cecf,
title = "Milnor invariants and the HOMFLYPT polynomial",
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.",
author = "Meilhan, {Jean Baptiste} and Akira Yasuhara",
year = "2012",
month = "7",
day = "9",
doi = "10.2140/gt.2012.16.889",
language = "English",
volume = "16",
pages = "889--917",
journal = "Geometry and Topology",
issn = "1465-3060",
publisher = "University of Warwick",
number = "2",

}

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 -