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.
Minhyong Kim, Arithmetic Chern-Simons Theory I, (arXiv:1510.05818).
Hee-Joong Chung, Dohyeong Kim, Minhyong Kim, Jeehoon Park, Hwajong Yoo, Arithmetic Chern-Simons Theory II, (arXiv:1609.03012)
Frauke M. Bleher, Ted Chinburg, Ralph Greenberg, Mahesh Kakde, George Pappas, Martin J. Taylor, Unramified arithmetic Chern-Simons invariants, (arXiv:1705.07110)
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.