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arXiv · 1511.06724

The cardinality of the augmentation category of a Legendrian link

Lenhard Ng·Dan Rutherford·Vivek Shende·Steven Sivek
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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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Lenhard Ng, Dan Rutherford, Vivek Shende, Steven Sivek. 2015-11-20. The cardinality of the augmentation category of a Legendrian link. https://doi.org/10.4310/mrl.2017.v24.n6.a14

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