Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: HOMFLY-PT polynomial and normal rulings of Legendrian solid torus links   We show that for any Legendrian link $L$ in the $1$-jet space of $S^1$ the
$2$-graded ruling polynomial, $R^2_L(z)$, is determined by the
Thurston-Bennequin number and the HOMFLY-PT polynomial. Specifically, we
recover $R^2_L(z)$ as a coefficient of a particular specialization of the
HOMFLY-PT polynomial. Furthermore, we show that this specialization may be
interpreted as the standard inner product on the algebra of symmetric functions
that is often identified with a certain subalgebra of the HOMFLY-PT skein
module of the solid torus.
  In contrast to the $2$-graded case, we are able to use $0$-graded ruling
polynomials to distinguish many homotopically non-trivial Legendrian links with
identical classical invariants.

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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg