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Publications [#355087] of Lenhard L. Ng
Papers Published
 Ng, L; Rutherford, D; Shende, V; Sivek, S; Zaslow, E, Augmentations are Sheaves,
Geometry and Topology, vol. 24 no. 5
(December, 2020),
pp. 21492286, Mathematical Sciences Publishers [doi]
(last updated on 2021/05/13)
Abstract: We show that the set of augmentations of the ChekanovEliashberg algebra of a
Legendrian link underlies the structure of a unital Ainfinity category. This
differs from the nonunital 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 xline, 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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