Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differential algebras of Legendrian links   The problem of classification of Legendrian knots (links) up to isotopy in
the class of Legendrian embeddings (Legendrian isotopy) naturally leads to the
following two subproblems. The first of them is: which combinations of the
three classical invariants can be realized by a Legendrian knot? (It is
well-known that each invariant by itself can be realized by a Legendrian knot).
The first step in this direction was done by Bennequin who proved that the
Bennequin number of a Legendrian knot is less than twice its genus.
  The second subproblem is whether there exist a pair of Legendrian knots which
have the same classical invariants but are not Legendrian isotopic. Eliashberg
and Fraser showed that this is impossible when knots are trivial as smooth
knots. In the present paper, we develop a theory which allows us, in
particular, to find a counterexample to this subproblem.

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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: econ