Publications [#355087] of Lenhard L. Ng

Papers Published

1. Ng, L; Rutherford, D; Shende, V; Sivek, S; Zaslow, E, Augmentations are sheaves, Geometry and Topology, vol. 24 no. 5 (January, 2020), pp. 2149-2286, Mathematical Sciences Publishers [doi]
   (last updated on 2025/03/13)

   Abstract:
   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.