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arXiv · 1706.03336

Abelian arithmetic Chern-Simons theory and arithmetic linking numbers

Hee-Joong Chung·Dohyeong Kim·Minhyong Kim·George Pappas·Jeehoon Park·Hwajong Yoo
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Abstract

Following the method of Seifert surfaces in knot theory, we define arithmetic linking numbers and height pairings of ideals using arithmetic duality theorems, and compute them in terms of n-th power residue symbols. This formalism leads to a precise arithmetic analogue of a 'path-integral formula' for linking numbers.

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Hee-Joong Chung, Dohyeong Kim, Minhyong Kim, George Pappas, Jeehoon Park, Hwajong Yoo. 2017-06-11. Abelian arithmetic Chern-Simons theory and arithmetic linking numbers. https://arxiv.org/abs/1706.03336

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