arXiv subjects

Hirofumi Niibo

Publications and source records attributed to Hirofumi Niibo.

3 recordsLinked to original sources

arXiv2022

A Hilbert reciprocity law on 3-manifolds

Based on our homological idelic class field theory, we formulate an analogue of the Hilbert reciprocity law on a rational homology 3-sphere endowed with an infinite link, in the spirit of arithmetic topology; We regard the intersection form on the unitary normal bundle of each knot as an analogue of the Hilbert symbol at each prime ideal to formulate the Hilbert reciprocity law, ensuring that cyclic covers of links are analogues of Kummer extensions.

math.GT↗

arXiv2016

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

We study a topological analogue of idèlic class field theory for 3-manifolds, in the spirit of arithmetic topology. We firstly 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.

math.GT↗

arXiv2013

Idèlic class field theory for 3-manifolds

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 $M$.

math.GT↗