Idèlic class field theory for 3-manifolds and very admissible links

Niibo, Hirofumi; Ueki, Jun

doi:10.1090/tran/7480

Idèlic class field theory for 3-manifolds and very admissible links
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by Hirofumi Niibo and Jun Ueki PDF

Trans. Amer. Math. Soc. 371 (2019), 8467-8488 Request permission

Abstract:

We study a topological analogue of idèlic class field theory for 3-manifolds in the spirit of arithmetic topology. We first introduce the notion of a very admissible link $\mathcal {K}$ in a 3-manifold $M$, which plays a role analogous to the set of primes of a number field. For such a pair $(M,\mathcal {K})$, we introduce the notion of idèles and define the idèle class group. Then, getting the local class field theory for each knot in $\mathcal {K}$ together, we establish analogues of the global reciprocity law and the existence theorem of idèlic class field theory.

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