Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Legendrian Ambient Surgery and Legendrian Contact Homology   Let $L \subset Y$ be a Legendrian submanifold of a contact manifold,
$S\subset L$ a framed embedded sphere bounding an isotropic disc $D_S \subset Y
\setminus L$, and use $L_S$ to denote the manifold obtained from $L$ by a
surgery on $S$. Given some additional conditions on $D_S$ we describe how to
obtain a Legendrian embedding of $L_S$ into an arbitrarily small neighbourhood
of $L \cup D_S \subset Y$ by a construction that we call Legendrian ambient
surgery. In the case when the disc is subcritical, we produce an isomorphism of
the Chekanov-Eliashberg algebra of $L_S$ with a version of the
Chekanov-Eliashberg algebra of $L$ whose differential is twisted by a count of
pseudo-holomorphic discs with boundary-point constraints on $S$. This
isomorphism induces a one-to-one correspondence between the augmentations of
the Chekanov-Eliashberg algebras of $L$ and $L_S$.

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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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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: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: math-ph
1
The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph