The quadratic linking degree
Algebraic Geometry
2025-08-05 v6 Geometric Topology
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.
Cite
@article{arxiv.2210.11048,
title = {The quadratic linking degree},
author = {Clémentine Lemarié--Rieusset},
journal= {arXiv preprint arXiv:2210.11048},
year = {2025}
}
Comments
Accepted by the Annales de l'Institut Fourier