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• W2949660018 abstract "Mazur, Kapranov, Reznikov, and others developed ``Arithmetic Topology,'' a theory describing some surprising analogies between 3-dimensional topology and number theory, which can be summarized by saying that knots are like prime numbers. We extend their work by proving several formulas concerning branched coverings of 3-manifolds and extensions of number fields and observe that these formulas are almost identical, via the dictionary of arithmetic topology. Until now there is no satisfactory explanation for the coincidences between our formulas. The proofs of topological results use equivariant cohomology and the Leray-Serre spectral sequence. The number theoretic proofs are based on an approach to class field theory via idele groups." @default.
• W2949660018 created "2019-06-27" @default.
• W2949660018 creator A5005209997 @default.
• W2949660018 date "2001-07-29" @default.
• W2949660018 modified "2023-09-27" @default.
• W2949660018 title "Analogies between group actions on 3-manifolds and number fields" @default.
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