On genus theory for 3-manifolds in arithmetic topology

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.