Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Alexander polynomial and the signature invariant of two-bridge
  knots   Fox conjectured the Alexander polynomial of an alternating knot is
trapezoidal, i.e. the coefficients first increase, then stabilize and finally
decrease in a symmetric way. Recently, Hirasawa and Murasugi further
conjectured a relation between the number of the stable coefficients in the
Alexander polynomial and the signature invariant. In this paper we prove the
Hirasawa-Murasugi conjecture for two-bridge knots.

11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci