Abelian quotients of the string link monoid

Jean Baptiste Meilhan, Akira Yasuhara

Research output: Contribution to journalArticlepeer-review


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
Issue number3
Publication statusPublished - 2014 Apr 7
Externally publishedYes

ASJC Scopus subject areas

  • Geometry and Topology


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