Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 213 (2014), 21-39.
On the homology of branched coverings of 3-manifolds
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.
Nagoya Math. J., Volume 213 (2014), 21-39.
First available in Project Euclid: 26 November 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M12: Special coverings, e.g. branched
Secondary: 12G05: Galois cohomology [See also 14F22, 16Hxx, 16K50] 52M27 11R29: Class numbers, class groups, discriminants 11R32: Galois theory
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