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arithmetic Chern-Simons theory

Contents

Idea

Arithmetic Chern-Simons theory names the attempt to apply constructions from Chern-Simons theory to the field of arithmetic, in view of patterns in the function field analogy. In particular, the papers (Kim1, Kim2) apply ideas of Dijkgraaf-Witten theory on 2+1 dimensional topological quantum field theory to arithmetic curves, that is, the spectra of rings of integers in algebraic number fields.

This theory pursues the surprising analogies between 3-dimensional topology and number theory, where knots embedded in a 3-manifold behave like prime ideals in a ring of algebraic integers, known as arithmetic topology.

References

For an introductory talk see

Last revised on December 17, 2017 at 18:24:07. See the history of this page for a list of all contributions to it.