THE QUADRATIC LINKING DEGREE

Clémentine Lemarié--Rieusset (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

By using motivic homotopy theory, we introduce an analogue in algebraic geometry of oriented links and their linking numbers. After constructing the 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.

Mots clés: Motivic homotopy theory; Knot theory; Links; Witt groups; Milnor-Witt K-theory

Domaines: Géométrie algébrique [math.AG]; Topologie géométrique [math.GT]

Clémentine Lemarié--Rieusset. THE QUADRATIC LINKING DEGREE. 2022. ⟨hal-03821736v2⟩