Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isotopies of Legendrian 1-knots and Legendrian 2-tori   We construct a Legendrian 2-torus in the 1-jet space of $S^1\times\R$ (or of
$\R^2$) from a loop of Legendrian knots in the 1-jet space of $\R$. The
differential graded algebra (DGA) for the Legendrian contact homology of the
torus is explicitly computed in terms of the DGA of the knot and the monodromy
operator of the loop. The contact homology of the torus is shown to depend only
on the chain homotopy type of the monodromy operator. The construction leads to
many new examples of Legendrian knotted tori. In particular, it allows us to
construct a Legendrian torus with DGA which does not admit any augmentation
(linearization) but which still has non-trivial homology, as well as two
Legendrian tori with isomorphic linearized contact homologies but with distinct
contact homologies.

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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: comp-gas