Nagoya Mathematical Journal

On the homology of branched coverings of 3-manifolds

Jun Ueki

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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

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

First available in Project Euclid: 26 November 2013

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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.

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