Augmentations are Sheaves
| dc.contributor.author | Ng, L | |
| dc.contributor.author | Rutherford, D | |
| dc.contributor.author | Shende, V | |
| dc.contributor.author | Sivek, S | |
| dc.contributor.author | Zaslow, E | |
| dc.date.accessioned | 2016-12-12T16:37:55Z | |
| dc.description.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. | |
| dc.format.extent | 102 pages | |
| dc.identifier | ||
| dc.identifier.uri | ||
| dc.publisher | Mathematical Sciences Publishers | |
| dc.subject | math.SG | |
| dc.subject | math.SG | |
| dc.subject | math.GT | |
| dc.title | Augmentations are Sheaves | |
| dc.type | Journal article | |
| duke.contributor.orcid | Ng, L|0000-0002-2443-5696 | |
| pubs.author-url | ||
| pubs.notes | v2: added Legendrian mirror example in section 4.4.4, corrected typos and other minor changes | |
| pubs.organisational-group | Duke | |
| pubs.organisational-group | Mathematics | |
| pubs.organisational-group | Trinity College of Arts & Sciences | |
| pubs.publication-status | Submitted |