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

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.

16 pages, 8 figures

Cited by in corpus (1)

• Milnor invariants, $2n$-moves and $V^n$-moves for welded string links