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Arithmetic topology is an area of mathematics that is a combination of algebraic number theory and topology. It establishes an analogy between number fields and closed, orientable 3-manifolds.

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Questions about analogy between Spec Z and 3-manifolds

There are some cryptic remarks about this in the first few pages of this talk of Fujiwara: http://www.ms.u-tokyo.ac.jp/~t-saito/conf/rv/Leopoldt.pdf (n.b. I believe - though I'm not 100% sure - that …
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