Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hilbert reciprocity law on 3-manifolds   Based on our homological idelic class field theory, we formulate an analogue
of the Hilbert reciprocity law for 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.

9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom