Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The degree of the colored HOMFLY polynomial   The colored HOMLFY polynomial is an important knot invariant depending on two
variables $a$ and $q$. We give bounds on the degree in both $a$ and $q$
generalizing Morton's bounds \cite{Mo86} for the ordinary HOMFLY polynomial.
Our bounds suggest that the degree detects certain incompressible surfaces in
the knot complement and perhaps more generally features of the $SL(N)$
character varieties of the knot group. We formulate a precise conjecture along
these lines generalizing the slope conjecture of Garoufalidis \cite{Ga11}. We
prove our conjecture for all positive knots.
  Our technique is a reformulation of the MOY state sum \cite{MOY98} using
$q$-analogues of Ehrhart polynomials. As a direct application we explicitly
compute the $r$ coefficients of $r$-colored HOMFLY polynomial of any positive
braid.

18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph