2019/11/29 by Hikaru Hirano, Hirano, Hikaru · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1911.12964
openalex publication_date 2019/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Minhyong Kim introduced arithmetic Chern-Simons invariants for totally imaginary number fields as arithmetic analogues of the Chern-Simons invariants for 3-manifolds. In this paper, we extend Kim's definition for any number field, by using the modified étale cohomology groups and fundamental groups which take real places into account. We then show explicit formulas of mod 2 arithmetic Dijkgraaf-Witten invariants for real quadratic fields ℚ (√(p1 p2 ⋯ pr)), where pi is a prime number congruent to 1 mod 4, in terms of the Legendre symbols of pi's. We also show topological analogues of our formulas for 3-manifolds.