no. 3
Classification of string links up to 2n-moves and link-homotopy
[Classification des enlacements d’intervalles à 2n-mouvements et homotopie près]
Miyazawa, Haruko A.1 ; Wada, Kodai2 ; Yasuhara, Akira3
1 Institute for Mathematics and Computer Science Tsuda University 2-1-1 Tsuda-machi, Kodaira Tokyo 187-8577 (Japan)
2 Department of Mathematics Kobe University 1-1 Rokkodai-cho, Nada-ku Kobe 657-8501 (Japan)
3 Faculty of Commerce Waseda University 1-6-1 Nishi-Waseda, Shinjuku-ku Tokyo 169-8050 (Japan)
Annales de l'Institut Fourier, Tome 71 (2021) no. 3, pp. 889-911.

Deux enlacements d’intervalles sont équivalents à 2n-mouvements et homotopie près si et seulement si leurs invariants d’homotopie de Milnor sont congrus modulo n. De plus, l’ensemble des classes d’équivalence forme un groupe fini engendré par des éléments d’ordre n. Cette classification implique que si deux enlacements d’intervalles sont équivalents à 2n-mouvements près pour tout n>0, alors ils sont homotopes.

Two string links are equivalent up to 2n-moves and link-homotopy if and only if their all Milnor link-homotopy invariants are congruent modulo n. Moreover, the set of the equivalence classes forms a finite group generated by elements of order n. The classification induces that if two string links are equivalent up to 2n-moves for every n>0, then they are link-homotopic.

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DOI : 10.5802/aif.3407
Classification : 57K10
Keywords: Milnor invariant, link, string link, $2n$-move, link-homotopy, Fox’s congruence class, clasper
Mot clés : Invariants de Milnor, entrelacs, enlacements d’intervalles, $2n$-mouvements, homotopie, classes de congruence de Fox, claspers

Miyazawa, Haruko A. 1 ; Wada, Kodai 2 ; Yasuhara, Akira 3

1 Institute for Mathematics and Computer Science Tsuda University 2-1-1 Tsuda-machi, Kodaira Tokyo 187-8577 (Japan)
2 Department of Mathematics Kobe University 1-1 Rokkodai-cho, Nada-ku Kobe 657-8501 (Japan)
3 Faculty of Commerce Waseda University 1-6-1 Nishi-Waseda, Shinjuku-ku Tokyo 169-8050 (Japan)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Classification of string links up to $2n$-moves and link-homotopy},
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Miyazawa, Haruko A.; Wada, Kodai; Yasuhara, Akira. Classification of string links up to $2n$-moves and link-homotopy. Annales de l'Institut Fourier, Tome 71 (2021) no. 3, pp. 889-911. doi : 10.5802/aif.3407. https://aif.centre-mersenne.org/articles/10.5802/aif.3407/

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