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arXiv · 2210.11048

The quadratic linking degree

Clémentine Lemarié--Rieusset
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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.

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Clémentine Lemarié--Rieusset. 2022-10-20. The quadratic linking degree. https://arxiv.org/abs/2210.11048

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