Augmentations and Legendrians at the IAS

Toward a contact Fukaya category

I will describe some work in progress (maybe more accurately, wild speculation) regarding a version of the derived Fukaya category for contact 1-jet spaces $J^1(X)$. This category is built from Legendrian submanifolds equipped with augmentations, and the full subcategory corresponding to a fixed Legendrian submanifold $\Lambda$ is the augmentation category $Aug(\Lambda)$, which I will attempt to review. The derived Fukaya category is generated by unknots, with the corollary that all augmentations ``come from unknot fillings''. I will also describe a potential application to proving that ``augmentations = sheaves''. This is work in progress with Tobias Ekholm and Vivek Shende, building on joint work with Dan Rutherford, Vivek Shende, Steven Sivek, and Eric Zaslow.

Date & Time

February 11, 2016 | 1:00pm – 2:00pm

Location

S-101

Speakers

Lenny Ng

Affiliation

Duke University

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