Idelic class field theory for 3-manifolds and very admissible links
Idelic class field theory for 3-manifolds and very admissible links
复制标题
三流形的理想类场论和非常可接受的联系
DOI：
10.1090/tran/7480
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Jun Ueki
中科院分区：
文献类型：
--
作者：
Hirofumi Niibo;Jun Ueki
我们本着算术拓扑的精神研究了3流形的id<s:1>类场理论的拓扑类比。我们首先引入了3流形上的极容许连杆的概念，它的作用类似于一个数域的素数集。对于这样的一对，我们引入id<e:1>的概念并定义id<e:1>类组。然后，将每个结点的局部类场论结合起来，建立了全局互易律的类似物和局部类场论的存在性定理。参考文献
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 linkin a 3-manifold, which plays a role analogous to the set of primes of a number field. For such a pair, we introduce the notion of idèles and define the idèle class group. Then, getting the local class field theory for each knot intogether, we establish analogues of the global reciprocity law and the existence theorem of idèlic class field theory. References