Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The C-polynomial of a knot   In an earlier paper the first author defined a non-commutative A-polynomial
for knots in 3-space, using the colored Jones function. The idea is that the
colored Jones function of a knot satisfies a non-trivial linear q-difference
equation. Said differently, the colored Jones function of a knot is annihilated
by a non-zero ideal of the Weyl algebra which is generalted (after
localization) by the non-commutative A-polynomial of a knot.
  In that paper, it was conjectured that this polynomial (which has to do with
representations of the quantum group U_q(SL_2)) specializes at q=1 to the
better known A-polynomial of a knot, which has to do with genuine SL_2(C)
representations of the knot complement.
  Computing the non-commutative A-polynomial of a knot is a difficult task
which so far has been achieved for the two simplest knots. In the present
paper, we introduce the C-polynomial of a knot, along with its non-commutative
version, and give an explicit computation for all twist knots. In a forthcoming
paper, we will use this information to compute the non-commutative A-polynomial
of twist knots. Finally, we formulate a number of conjectures relating the A,
the C-polynomial and the Alexander polynomial, all confirmed for the class of
twist knots.

23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph