Classification of string links up to self delta-moves and concordance

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

For an n-component string link, the Milnor's concordance invariant is defined for each sequence I = i1i2...im(ij,in {1,...,n}) Let r(I) denote the maximum number of times that any index appears. We show that two string links are equivalent up to self Δ-moves and concordance if and only if their Milnor invariants coincide for all sequences I with r(I) ≤ 2.

Original languageEnglish
Pages (from-to)265-275
Number of pages11
JournalAlgebraic and Geometric Topology
Volume9
Issue number1
DOIs
Publication statusPublished - 2009 Dec 1
Externally publishedYes

Fingerprint

Concordance
Strings
Invariant
If and only if
Denote

Keywords

  • Δ-move
  • Concordance
  • Link-homotopy
  • Milnor invariant
  • Self Δ-equivalence
  • Self Δ-move
  • String link

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Classification of string links up to self delta-moves and concordance. / Yasuhara, Akira.

In: Algebraic and Geometric Topology, Vol. 9, No. 1, 01.12.2009, p. 265-275.

Research output: Contribution to journalArticle

@article{729df7029c204b439ea17c2517a73950,
title = "Classification of string links up to self delta-moves and concordance",
abstract = "For an n-component string link, the Milnor's concordance invariant is defined for each sequence I = i1i2...im(ij,in {1,...,n}) Let r(I) denote the maximum number of times that any index appears. We show that two string links are equivalent up to self Δ-moves and concordance if and only if their Milnor invariants coincide for all sequences I with r(I) ≤ 2.",
keywords = "Δ-move, Concordance, Link-homotopy, Milnor invariant, Self Δ-equivalence, Self Δ-move, String link",
author = "Akira Yasuhara",
year = "2009",
month = "12",
day = "1",
doi = "10.2140/agt.2009.9.265",
language = "English",
volume = "9",
pages = "265--275",
journal = "Algebraic and Geometric Topology",
issn = "1472-2747",
publisher = "Agriculture.gr",
number = "1",

}

TY - JOUR

T1 - Classification of string links up to self delta-moves and concordance

AU - Yasuhara, Akira

PY - 2009/12/1

Y1 - 2009/12/1

N2 - For an n-component string link, the Milnor's concordance invariant is defined for each sequence I = i1i2...im(ij,in {1,...,n}) Let r(I) denote the maximum number of times that any index appears. We show that two string links are equivalent up to self Δ-moves and concordance if and only if their Milnor invariants coincide for all sequences I with r(I) ≤ 2.

AB - For an n-component string link, the Milnor's concordance invariant is defined for each sequence I = i1i2...im(ij,in {1,...,n}) Let r(I) denote the maximum number of times that any index appears. We show that two string links are equivalent up to self Δ-moves and concordance if and only if their Milnor invariants coincide for all sequences I with r(I) ≤ 2.

KW - Δ-move

KW - Concordance

KW - Link-homotopy

KW - Milnor invariant

KW - Self Δ-equivalence

KW - Self Δ-move

KW - String link

UR - http://www.scopus.com/inward/record.url?scp=72949115290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=72949115290&partnerID=8YFLogxK

U2 - 10.2140/agt.2009.9.265

DO - 10.2140/agt.2009.9.265

M3 - Article

VL - 9

SP - 265

EP - 275

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

SN - 1472-2747

IS - 1

ER -