The cardinality of the augmentation category of a Legendrian link

@article{Ng2017TheCO,
  title={The cardinality of the augmentation category of a Legendrian link},
  author={L. Ng and D. Rutherford and V. Shende and Steven Sivek},
  journal={Mathematical Research Letters},
  year={2017},
  volume={24},
  pages={1845-1874}
}
  • L. Ng, D. Rutherford, +1 author Steven Sivek
  • Published 2017
  • Mathematics
  • Mathematical Research Letters
  • 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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