Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a Poincar\'e polynomial from Khovanov homology and Vassiliev
  invariants   We introduce a Poincar\'{e} polynomial with two-variable $t$ and $x$ for
knots, derived from Khovanov homology, where the specialization $(t, x)$ $=$
$(1, -1)$ is a Vassiliev invariant of order $n$. Since for every $n$, there
exist non-trivial knots with the same value of the Vassiliev invariant of order
$n$ as that of the unknot, there has been no explicit formulation of a
perturbative knot invariant which is a coefficient of $y^n$ by the replacement
$q=e^y$ for the quantum parameter $q$ of a quantum knot invariant, and which
distinguishes the above knots together with the unknot. The first formulation
is our polynomial.

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The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio