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Cohomological Approach to Class Field Theory in Arithmetic Topology

Part of: Categories and geometry Generalized manifolds Miscellaneous applications of number theory Homology and cohomology theories

Published online by Cambridge University Press:  09 January 2019

Tomoki Mihara
Tomoki Mihara*
Affiliation:
Tsukuba University, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan Email: mihara@math.tsukuba.ac.jp
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Abstract

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We establish class field theory for three-dimensional manifolds and knots. For this purpose, we formulate analogues of the multiplicative group, the idèle class group, and ray class groups in a cocycle-theoretic way. Following the arguments in abstract class field theory, we construct reciprocity maps and verify the existence theorems.

Keywords

Arithmetic topologyclass field theorybranched coveringknots and prime numbers

MSC classification

Primary: 11Z05: Miscellaneous applications of number theory
Secondary: 18F15: Abstract manifolds and fiber bundles 55N20: Generalized (extraordinary) homology and cohomology theories 57P05: Local properties of generalized manifolds
Type
Article
Information
Canadian Journal of Mathematics , Volume 71 , Issue 4 , August 2019 , pp. 891 - 935
Copyright
© Canadian Mathematical Society 2018 

References

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