The cardinality of the augmentation category of a Legendrian link
Symplectic Geometry
2018-01-31 v1 Geometric Topology
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.
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Cite
@article{arxiv.1511.06724,
title = {The cardinality of the augmentation category of a Legendrian link},
author = {Lenhard Ng and Dan Rutherford and Vivek Shende and Steven Sivek},
journal= {arXiv preprint arXiv:1511.06724},
year = {2018}
}
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15 pages