2022/10/20 by Clémentine Lemarié--Rieusset, Lemarié--Rieusset, Clémentine
Mathematics · #14C25 #14F42 #19E15 (Secondary) #57K10 (Primary) 11E81 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · doi:10.48550/arxiv.2210.11048
openalex publication_date 2022/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.