hal-03821736
https://u-bourgogne.hal.science/hal-03821736
https://u-bourgogne.hal.science/hal-03821736v2/document
https://u-bourgogne.hal.science/hal-03821736v2/file/The%20quadratic%20linking%20degree.pdf
arxiv:2210.11048
THE QUADRATIC LINKING DEGREE
Lemarié--Rieusset, Clémentine
[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]
[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
UNDEFINED
Motivic homotopy theory
Knot theory
Links
Witt groups
Milnor-Witt K-theory
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.
2022-12-15
2022-12-15
en