Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representations of knot groups into $\mathrm{SL}_n(\mathbf{C})$ and
  twisted Alexander polynomials   Let $\Gamma$ be the fundamental group of the exterior of a knot in the
three-sphere. We study deformations of representations of $\Gamma$ into
$\mathrm{SL}_n(\mathbf{C})$ which are the sum of two irreducible
representations. For such representations we give a necessary condition, in
terms of the twisted Alexander polynomial, for the existence of irreducible
deformations. We also give a more restrictive sufficient condition for the
existence of irreducible deformations. We also prove a duality theorem for
twisted Alexander polynomials and we describe the local structure of the
representation and character varieties.

1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc