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Augmentations are Sheaves
File | Description | Size | Format | |
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augmain.pdf | Accepted version | 969.19 kB | Adobe PDF | View/Open |
Title: | Augmentations are Sheaves |
Authors: | Ng, L Rutherford, D Shende, V Sivek, S Zaslow, E |
Item Type: | Journal Article |
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. |
Issue Date: | 29-Dec-2020 |
Date of Acceptance: | 7-Dec-2019 |
URI: | http://hdl.handle.net/10044/1/75472 |
DOI: | 10.2140/gt.2020.24.2149 |
ISSN: | 1364-0380 |
Publisher: | Mathematical Sciences Publishers |
Start Page: | 2149 |
End Page: | 2286 |
Journal / Book Title: | Geometry and Topology |
Volume: | 24 |
Issue: | 5 |
Copyright Statement: | © Copyright 2020 Mathematical Sciences Publishers. All rights reserved. |
Keywords: | math.SG math.SG math.GT math.SG math.SG math.GT 0101 Pure Mathematics Geological & Geomatics Engineering |
Notes: | 102 pages; v2: added Legendrian mirror example in section 4.4.4, corrected typos and other minor changes |
Publication Status: | Published |
Online Publication Date: | 2020-12-29 |
Appears in Collections: | Pure Mathematics Faculty of Natural Sciences Mathematics |