The cardinality of the augmentation category of a Legendrian link
File(s)counting.pdf (369.19 KB)
Accepted version
Author(s)
Ng, Lenhard
Rutherford, Dan
Shende, Vivek
Sivek, Steven
Type
Working Paper
Abstract
We introduce a notion of cardinality for the augmentation category associated
to a Legendrian knot or link in standard contact R^3. This `homotopy
cardinality' is an invariant of the category and allows for a weighted count of
augmentations, which we prove to be determined by the ruling polynomial of the
link. We present an application to the augmentation category of doubly
Lagrangian slice knots.
to a Legendrian knot or link in standard contact R^3. This `homotopy
cardinality' is an invariant of the category and allows for a weighted count of
augmentations, which we prove to be determined by the ruling polynomial of the
link. We present an application to the augmentation category of doubly
Lagrangian slice knots.
Date Issued
2017-12-31
Date Acceptance
2016-06-04
Citation
Mathematical Research Letters, 24 (6), pp.1845-1874
ISSN
1073-2780
Publisher
International Press
Start Page
1845
End Page
1874
Journal / Book Title
Mathematical Research Letters
Volume
24
Issue
6
Copyright Statement
© 2015 The Authors
Identifier
http://arxiv.org/abs/1511.06724v1
Subjects
math.SG
math.SG
math.GT
Notes
15 pages
Date Publish Online
2018-01-29