The quadratic linking degree

By using motivic homotopy theory, we introduce a counterpart in algebraic geometry to oriented links and their linking numbers. After constructing the (ambient) quadratic linking degree — our analogue of the linking number which takes values in the Witt group of the ground field — and exploring some of its properties, we give a method to explicitly compute it. We illustrate this method on a family of examples which are analogues of torus links, in particular of the Hopf and Solomon links.

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Publication Details

Journal
Annales de l’institut Fourier
Published
2026-03-26
DOI
https://doi.org/10.5802/aif.3776
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
article
Field-Weighted Citation Impact
0.00
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article

The quadratic linking degree

Annales de l’institut Fourier
Homotopy and Cohomology in Algebraic Topology
article

The quadratic linking degree

article en

Abstract

By using motivic homotopy theory, we introduce a counterpart in algebraic geometry to oriented links and their linking numbers. After constructing the (ambient) quadratic linking degree — our analogue of the linking number which takes values in the Witt group of the ground field — and exploring some of its properties, we give a method to explicitly compute it. We illustrate this method on a family of examples which are analogues of torus links, in particular of the Hopf and Solomon links.

Annales de l’institut Fourier
Centre National de la Recherche Scientifique (FR), Institut de Mathématiques de Bourgogne (FR), University of Duisburg-Essen (DE)
Openalex Percentile: Top 5%
Homotopy and Cohomology in Algebraic Topology
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