Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A novel connection between integral binary quadratic forms and knot
  polynomials   We establish a novel connection between algebraic number theory and knot
theory. We show that the number of equivalence classes of integral binary
quadratic forms of discriminant $t^2 - 4$ (for $t\neq \pm 2$) is equal to the
number of isotopy classes of links in $\mathbb{S}^3$ with prescribed values
(depending on $t$) of three classical link invariants. The equality arises from
a natural algebraic correspondence between integral binary quadratic forms (of
discriminant $t^2 - 4$ for $t\neq \pm 2$) and isotopy classes of links of braid
index at most three. In particular, the class numbers of certain quadratic
number fields precisely measure the failure of the Alexander/Jones polynomial
to distinguish non-isotopic links of braid index at most three.

1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom