Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Augmentations are Sheaves   We show that the set of augmentations of the Chekanov-Eliashberg algebra of a
Legendrian link underlies the structure of a unital A-infinity category. This
differs from the non-unital category constructed in [BC], but is related to it
in the same way that cohomology is related to compactly supported cohomology.
The existence of such a category was predicted by [STZ], who moreover
conjectured its equivalence to a category of sheaves on the front plane with
singular support meeting infinity in the knot. After showing that the
augmentation category forms a sheaf over the x-line, we are able to prove this
conjecture by calculating both categories on thin slices of the front plane. In
particular, we conclude that every augmentation comes from geometry.

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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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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: nlin
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The categories of this paper are: dg-ga