  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.
