Work

The quadratic linking degree

Year: 2026

Type: article

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.

Source: Annales de l’institut Fourier

DOI: 10.5802/aif.3776

Author: Clémentine Lemarié--Rieusset

Institutions: Centre National de la Recherche Scientifique, Université de Bourgogne, Institut de Mathématiques de Bourgogne, University of Duisburg-Essen

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Deutsche Forschungsgemeinschaft, Agence Nationale de la Recherche

Awards: G2659019386, Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité, G6803667113, Motivic homotopy, quadratic invariants and diagonal classes