2021/06/04 by Hikaru Hirano, Hirano, Hikaru, Kim Junhyeong +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2106.02308
openalex publication_date 2021/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present basic constructions and properties in arithmetic Chern-Simons theory with finite gauge group along the line of topological quantum field theory. For a finite set S of finite primes of a number field k, we construct arithmetic analogues of the Chern-Simons 1-cocycle, the prequantization bundle for a surface and the Chern-Simons functional for a 3-manifold. We then construct arithmetic analogues for k and S of the quantum Hilbert space (space of conformal blocks) and the Dijkgraaf-Witten partition function in (2+1)-dimensional Chern-Simons TQFT. We show some basic and functorial properties of those arithmetic analogues. Finally we show decomposition and gluing formulas for arithmetic Chern-Simons invariants and arithmetic Dijkgraaf-Witten partition functions.