Idèlic class field theory for 3-manifolds

Hirofumi Niibo

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arXiv · 1311.5314

Idèlic class field theory for 3-manifolds

Hirofumi Niibo

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Abstract

Following the analogies between 3-dimensional topology and number theory, we study an idèlic form of class field theory for 3-manifolds. For a certain set $\mathcal{K}$ of knots in a 3-manifold $M$, we first present a local theory for each knot in $\mathcal{K}$, which is analogous to local class field theory, and then, getteing together over all knots in $\mathcal{K}$, we give an analogue of idèlic global class field theory for an integral homology sphere $M$.

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Hirofumi Niibo. 2013-12-11. Idèlic class field theory for 3-manifolds. https://arxiv.org/abs/1311.5314

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