On genus theory for 3-manifolds in arithmetic topology

2025/05/23 by Tashiro, Hirotaka
#11R37 #57M12 #FOS: Mathematics #Geometric Topology (math.GT) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.17486

Abstract

Based on the analogies of arithmetic topology, we show a topological analogue of Hilbert's Satz 90 for idele groups and utilize our previously established Hasse norm principle to present a proof of an Iyanaga--Tamagawa type genus formula for finite abelian branched covers over integral homology 3-spheres in a very parallel manner to the case of number theory.

Citations

• On Hasse norm principle for 3-manifolds in arithmetic topology
• Idèlic class field theory for 3-manifolds

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