Augmentations are Sheaves

Accepted

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Ng, L; Rutherford, D; Shende, V; Sivek, S; Zaslow, E

Published In

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International Standard Serial Number (ISSN)

  • 1364-0380