Contents Online
Mathematical Research Letters
Volume 24 (2017)
Number 6
The cardinality of the augmentation category of a Legendrian link
Pages: 1845 – 1874
DOI: https://dx.doi.org/10.4310/MRL.2017.v24.n6.a14
Authors
Abstract
We introduce a notion of cardinality for the augmentation category associated to a Legendrian knot or link in standard contact $\mathbb{R}^3$. 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.
Received 5 January 2016
Accepted 3 June 2016
Published 29 January 2018