Classification of string links up to $2n$-moves and link-homotopy

Haruko A. Miyazawa; Kodai Wada; Akira Yasuhara

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arXiv · 1902.06079

Classification of string links up to $2n$-moves and link-homotopy

Haruko A. Miyazawa·Kodai Wada·Akira Yasuhara

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Abstract

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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Haruko A. Miyazawa, Kodai Wada, Akira Yasuhara. 2019-02-16. Classification of string links up to $2n$-moves and link-homotopy. https://arxiv.org/abs/1902.06079

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