Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 14, Number 3 (2014), 1461-1488.
Abelian quotients of the string link monoid
The set of –string links has a monoid structure, given by the stacking product. When considered up to concordance, becomes a group, which is known to be abelian only if . In this paper, we consider two families of equivalence relations which endow with a group structure, namely the –equivalence introduced by Habiro in connection with finite-type invariants theory, and the –concordance, which is generated by –equivalence and concordance. We investigate under which condition these groups are abelian, and give applications to finite-type invariants.
Algebr. Geom. Topol., Volume 14, Number 3 (2014), 1461-1488.
Received: 7 May 2013
Revised: 31 October 2013
Accepted: 6 November 2013
First available in Project Euclid: 19 December 2017
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Meilhan, Jean-Baptiste; Yasuhara, Akira. Abelian quotients of the string link monoid. Algebr. Geom. Topol. 14 (2014), no. 3, 1461--1488. doi:10.2140/agt.2014.14.1461. https://projecteuclid.org/euclid.agt/1513715911