三维流形上的Hilbert倒易律
A Hilbert reciprocity law on 3-manifolds
摘要：
基于同调理想类域理论，我们在算术拓扑的思想下，在具有无限链环的有理同调三维球面上建立了Hilbert倒易律的一个类似形式;我们把每个纽结的酉法丛上的交形式看作是每个素理想上的Hilbert符号的模拟，从而建立了Hilbert互易律，确保链的循环覆盖是Kummer扩张的类似物。
英文摘要：
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.
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