Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the twisted Alexander polynomial for representations into SL_2(C)   We study the twisted Alexander polynomial $\Delta_{K,\rho}$ of a knot $K$
associated to a non-abelian representation $\rho$ of the knot group into
$SL_2(\BC)$. It is known for every knot $K$ that if $K$ is fibered, then for
every non-abelian representation, $\Delta_{K,\rho}$ is monic and has degree
$4g(K)-2$ where $g(K)$ is the genus of $K$. Kim and Morifuji recently proved
the converse for 2-bridge knots. In fact they proved a stronger result: if a
2-bridge knot $K$ is non-fibered, then all but finitely many non-abelian
representations on some component have $\Delta_{K,\rho}$ non-monic and degree
$4g(K)-2$. In this paper, we consider two special families of non-fibered
2-bridge knots including twist knots. For these families, we calculate the
number of non-abelian representations where $\Delta_{K,\rho}$ is monic and
calculate the number of non-abelian representations where the degree of
$\Delta_{K,\rho}$ is less than $4g(K)-2$.

31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs