## Nagoya Mathematical Journal

### On the homology of branched coverings of 3-manifolds

Jun Ueki

#### Abstract

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.

#### Article information

Source
Nagoya Math. J., Volume 213 (2014), 21-39.

Dates
First available in Project Euclid: 26 November 2013

https://projecteuclid.org/euclid.nmj/1385480157

Digital Object Identifier
doi:10.1215/00277630-2393795

Mathematical Reviews number (MathSciNet)
MR3290684

Zentralblatt MATH identifier
1295.57002

#### Citation

Ueki, Jun. On the homology of branched coverings of 3-manifolds. Nagoya Math. J. 213 (2014), 21--39. doi:10.1215/00277630-2393795. https://projecteuclid.org/euclid.nmj/1385480157

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