Algebraic Knots and their Universal K^MW_2-Coverings

Matthias Wendt; Thor Wittich

Algebraic Knots and their Universal K^MW_2-Coverings

Algebraic Geometry 2026-07-20 v1 Algebraic Topology K-Theory and Homology

Authors: Matthias Wendt , Thor Wittich

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.

Keywords

algebraic knots motivic homotopy theory K-theory universal coverings rectifiability invariant

Cite

@article{arxiv.2607.17716,
  title  = {Algebraic Knots and their Universal K^MW_2-Coverings},
  author = {Matthias Wendt and Thor Wittich},
  journal= {arXiv preprint arXiv:2607.17716},
  year   = {2026}
}

Comments

25 pages, 1 figure