Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A subtle new invariant for framed knots and links   We produce a facial state sum on plane diagrams of a knot or a link which
admits an invariant specialization under Polyak's recent set of generating of 4
Reidemeister moves. Thus an isotopy invariant of framed links is obtained. Each
state is a complete coloring of the faces of the diagram into white and black
faces so that no two black faces share an edge. Each state induces a monomial
in a ring of 16 variables. The sum of the states, properly specialized defines
the new invariant. In despite of its simplicity it complements Jones invariant
in distinguishing mirror pairs of links. In particular it proves that $9_{42}$
is distinct from its mirror image. For this pair of knots both the Jones
Polynomial and Kauffman 2-variable polynomial fail.

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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int