Relative knot concordance

Vyacheslav Krushkal; Ryan Stees

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arXiv · 2610.19467

Relative knot concordance

Vyacheslav Krushkal·Ryan Stees

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Abstract

Motivated by the relative-slice problem in $4$-manifold topology, we define for a knot $R$ the notion of a relative knot concordance group $\mathcal{C}_R$ and analyze the structure of its algebraic analogue $\mathcal{AC}_R$ modulo torsion. Using Milnor signatures, we show that $\mathcal{AC}_R$ has infinite rank for every $R$. We also show that any prescribed finite set of natural numbers can be realized as orders of elements in a single relative concordance group.

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Vyacheslav Krushkal, Ryan Stees. 2026-10-14. Relative knot concordance. https://arxiv.org/abs/2610.19467

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