Solvability of concordance groups and Milnor invariants

Alessio Di Prisa; Giovanni Framba

Solvability of concordance groups and Milnor invariants

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arxiv 2312.02058 v1 pith:Z3GD3NNW submitted 2023-12-04 math.GT

Alessio Di Prisa , Giovanni Framba This is my paper · ORCID

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keywords concordancegroupinvariantsmilnorprovesolvableanswerconjecture

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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 posed by Kuzbary.

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Equivariant Q-sliceness of strongly invertible knots
math.GT 2024-12 conditional novelty 5.0 of 10

The paper introduces equivariant Q-sliceness for strongly invertible knots, proves Klein amphichiral knots are equivariant Q-slice in a single Q-homology 4-ball, and shows Alexander polynomial squareness obstructs it.

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