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Abelian quotients of
the string link monoid
Jean-Baptiste Meilhan and Akira Yasuhara |
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Algebraic & Geometric Topology 14 (2014) 1461–1488
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Abstract |
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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. |
Keywords
string links, $C_n$–moves, concordance, claspers, Milnor
invariants
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Secondary: 20F38
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References |
Publication
Received: 7 May 2013
Revised: 31 October 2013
Accepted: 6 November 2013
Published: 7 April 2014
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Authors |
| Jean-Baptiste Meilhan | |
| Institut Fourier Université Grenoble 1 100 rue des Maths, BP 74 38402 Saint Martin d’Hères France |
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| http://www-fourier.ujf-grenoble.fr/~meilhan/ | |
| Akira Yasuhara | |
| Department of Mathematics Tokyo Gakugei University 4-1-1 Nukuikita-Machi Koganei-shi Tokyo 184-8501 Japan |
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| http://www.u-gakugei.ac.jp/~yasuhara/ | |
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