Solvability of concordance groups and Milnor invariants

Abstract

Using Milnor invariants, we prove that the concordance group $\mathcal{C}(2)$ of $2$-string links is not solvable. As a consequence, we prove that the equivariant concordance group of strongly invertible knots is also not solvable, and we answer a conjecture by Kuzbary (2023).