Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Irreducible $SL(2,\mathbb{C})$-metabelian representations of branched
  twist spins   An $(m,n)$-branched twist spin is a fibered $2$-knot in $S^4$ which is
determined by a $1$-knot $K$ and coprime integers $m$ and $n$. For a $1$-knot,
Lin proved that the number of irreducible $SL(2,\mathbb{C})$-metabelian
representations of the knot group of a $1$-knot up to conjugation is determined
by the knot determinant of the $1$-knot. In this paper, we prove that the
number of irreducible $SL(2,\mathbb{C})$-metabelian representations of the knot
group of an $(m,n)$-branched twist spin up to conjugation is determined by the
determinant of a $1$-knot in the orbit space by comparing a presentation of the
knot group of the branched twist spin with the Lin's presentation of the knot
group of the $1$-knot.

28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol