Algebraic Knots and their Universal K^MW₂-Coverings

2026/07/20 by Matthias Wendt, Thor Wittich · 1 voice
#math.AG #math.AT #math.KT

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Abstract

Over suitable base fields k of characteristic not 2, including algebraically closed ones, we construct universal abelian \underlineK^MW₂-coverings for complements of closed embeddings \mathbbA¹ \hookrightarrow \mathbbA³. Using these, we obtain a rectifiability invariant of such embeddings by lifting knot-theoretic ideas to algebraic geometry via motivic homotopy theory.

Citations

• The six operations in equivariant motivic homotopy theory

Discussions

• Did you see this paper on the arXiv yesterday? arxiv.org/abs/2607.17716 It uses techniques from motivic homotopy theory (my baby) to provide rectifiability invariants (in terms of first A^1-homology o [bsky, 10 points, 2 comments]

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