Abelian quotients of the string link monoid

Jean Baptiste Meilhan, Akira Yasuhara

Research output: Contribution to journalArticle

Abstract

The set SL(n) of n-string links has a monoid structure, given by the stacking product. When considered up to concordance, SL(n) becomes a group, which is known to be abelian only if nD1. In this paper, we consider two families of equivalence relations which endow SL. (n) with a group structure, namely the Ck-equivalence introduced by Habiro in connection with finite-type invariants theory, and the Ck-concordance, which is generated by Ck-equivalence and concordance. We investigate under which condition these groups are abelian, and give applications to finite-type invariants.

Original languageEnglish
Pages (from-to)1461-1488
Number of pages28
JournalAlgebraic and Geometric Topology
Volume14
Issue number3
DOIs
Publication statusPublished - 2014 Apr 7
Externally publishedYes

Fingerprint

Concordance
Monoid
Finite Type Invariants
Quotient
Strings
Equivalence
Invariant Theory
Type Theory
Stacking
Equivalence relation

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Abelian quotients of the string link monoid. / Meilhan, Jean Baptiste; Yasuhara, Akira.

In: Algebraic and Geometric Topology, Vol. 14, No. 3, 07.04.2014, p. 1461-1488.

Research output: Contribution to journalArticle

Meilhan, Jean Baptiste ; Yasuhara, Akira. / Abelian quotients of the string link monoid. In: Algebraic and Geometric Topology. 2014 ; Vol. 14, No. 3. pp. 1461-1488.
@article{93fe2e0b71864f2c99df3df8bef4a55f,
title = "Abelian quotients of the string link monoid",
abstract = "The set SL(n) of n-string links has a monoid structure, given by the stacking product. When considered up to concordance, SL(n) becomes a group, which is known to be abelian only if nD1. In this paper, we consider two families of equivalence relations which endow SL. (n) with a group structure, namely the Ck-equivalence introduced by Habiro in connection with finite-type invariants theory, and the Ck-concordance, which is generated by Ck-equivalence and concordance. We investigate under which condition these groups are abelian, and give applications to finite-type invariants.",
author = "Meilhan, {Jean Baptiste} and Akira Yasuhara",
year = "2014",
month = "4",
day = "7",
doi = "10.2140/agt.2014.14.1461",
language = "English",
volume = "14",
pages = "1461--1488",
journal = "Algebraic and Geometric Topology",
issn = "1472-2747",
publisher = "Agriculture.gr",
number = "3",

}

TY - JOUR

T1 - Abelian quotients of the string link monoid

AU - Meilhan, Jean Baptiste

AU - Yasuhara, Akira

PY - 2014/4/7

Y1 - 2014/4/7

N2 - The set SL(n) of n-string links has a monoid structure, given by the stacking product. When considered up to concordance, SL(n) becomes a group, which is known to be abelian only if nD1. In this paper, we consider two families of equivalence relations which endow SL. (n) with a group structure, namely the Ck-equivalence introduced by Habiro in connection with finite-type invariants theory, and the Ck-concordance, which is generated by Ck-equivalence and concordance. We investigate under which condition these groups are abelian, and give applications to finite-type invariants.

AB - The set SL(n) of n-string links has a monoid structure, given by the stacking product. When considered up to concordance, SL(n) becomes a group, which is known to be abelian only if nD1. In this paper, we consider two families of equivalence relations which endow SL. (n) with a group structure, namely the Ck-equivalence introduced by Habiro in connection with finite-type invariants theory, and the Ck-concordance, which is generated by Ck-equivalence and concordance. We investigate under which condition these groups are abelian, and give applications to finite-type invariants.

UR - http://www.scopus.com/inward/record.url?scp=84898481706&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898481706&partnerID=8YFLogxK

U2 - 10.2140/agt.2014.14.1461

DO - 10.2140/agt.2014.14.1461

M3 - Article

AN - SCOPUS:84898481706

VL - 14

SP - 1461

EP - 1488

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

SN - 1472-2747

IS - 3

ER -