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

Yuka Kotorii, Akira Yasuhara

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)87-100
Number of pages14
JournalTopology and its Applications
Volume184
DOIs
Publication statusPublished - 2015 Apr 1
Externally publishedYes

Fingerprint

Invariant
Knot
Vanish
Polynomial
Term

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.

In: Topology and its Applications, Vol. 184, 01.04.2015, p. 87-100.

Research output: Contribution to journalArticle

@article{cf9d8625b3fa453bac1534b9b1513144,
title = "Milnor invariants of length 2k+2 for links with vanishing Milnor invariants of length ≤k",
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.",
keywords = "Clasper, HOMFLYPT polynomial, Milnor μ--invariant",
author = "Yuka Kotorii and Akira Yasuhara",
year = "2015",
month = "4",
day = "1",
doi = "10.1016/j.topol.2015.01.003",
language = "English",
volume = "184",
pages = "87--100",
journal = "Topology and its Applications",
issn = "0166-8641",
publisher = "Elsevier",

}

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 -