The cardinality of the augmentation category of a Legendrian link
arXiv:1511.06724 · doi:10.4310/MRL.2017.v24.n6.a14
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.
15 pages