Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Evolution method and "differential hierarchy" of colored knot
  polynomials   We consider braids with repeating patterns inside arbitrary knots which
provides a multi-parametric family of knots, depending on the "evolution"
parameter, which controls the number of repetitions. The dependence of knot
(super)polynomials on such evolution parameters is very easy to find. We apply
this evolution method to study of the families of knots and links which include
the cases with just two parallel and anti-parallel strands in the braid, like
the ordinary twist and 2-strand torus knots/links and counter-oriented 2-strand
links. When the answers were available before, they are immediately reproduced,
and an essentially new example is added of the "double braid", which is a
combination of parallel and anti-parallel 2-strand braids. This study helps us
to reveal with the full clarity and partly investigate a mysterious
hierarchical structure of the colored HOMFLY polynomials, at least, in
(anti)symmetric representations, which extends the original observation for the
figure-eight knot to many (presumably all) knots. We demonstrate that this
structure is typically respected by the t-deformation to the superpolynomials.

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The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int