Following the analogies between 3-manifolds and number rings in arithmetic topology, we study the homology of branched covers of 3-manifolds. In particular, we show some analogues of Iwasawa’s theorems on ideal class groups and unit groups, Hilbert’s Satz 90, and some genus-theory–type results in the context of 3-dimensional topology. We also prove that the 2-cycles valued Tate cohomology of branched Galois covers is a topological invariant, and we give a new insight into the analogy between 2-cycle groups and unit groups.
Jun Ueki. "On the homology of branched coverings of 3-manifolds." Nagoya Math. J. 213 21 - 39, March 2014. https://doi.org/10.1215/00277630-2393795