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arXiv · 2607.17716

Algebraic Knots and their Universal K^MW_2-Coverings

Matthias Wendt·Thor Wittich
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Abstract

Over suitable base fields $k$ of characteristic not $2$, including algebraically closed ones, we construct universal abelian $\underline{\operatorname{K}}^{\operatorname{MW}}_2$-coverings for complements of closed embeddings $\mathbb{A}^1 \hookrightarrow \mathbb{A}^3$. Using these, we obtain a rectifiability invariant of such embeddings by lifting knot-theoretic ideas to algebraic geometry via motivic homotopy theory.

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Matthias Wendt, Thor Wittich. 2026-07-20. Algebraic Knots and their Universal K^MW_2-Coverings. https://arxiv.org/abs/2607.17716

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