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On the homology of branched coverings of 3-manifolds

Published online by Cambridge University Press:  11 January 2016

Jun Ueki
Jun Ueki*
Affiliation:
Graduate School of Mathematics Kyushu University, Fukuoka-city, Fukuoka, 819-0395, Japan, uekijun46@gmail.com
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Abstract

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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.

Keywords

57M1212G0552M2711R2911R32
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 213 , March 2014 , pp. 21 - 39
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

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