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

2019/02/16 by Haruko A. Miyazawa, Miyazawa, Haruko A., Kodai Wada +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #57M25 #57M27 #Cellular transport and secretion #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1902.06079

openalex publication_date 2019/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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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