Abelian Arithmetic Chern-Simons Theory and Arithmetic Linking Numbers

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. © The Author(s) 2017. Published by Oxford University Press. All rights reserved. For permissions,