Augmentations and immersed exact Lagrangian cobordisms

Augmentations and immersed exact Lagrangian cobordisms

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Yu Pan, Massachusetts Institute of Technology
Fine Hall 224

Not all the augmentations of a Legendrian knot come from embedded exact Lagrangian fillings. In this talk, we show that all the augmentations come from possibly immersed exact Lagrangian fillings. We first associate an immersed cobordism with  a DGA map from the top Legendrian knot to the DGA of the cobordism. This gives a functor from a Legendrian category whose morphisms involve immersed Lagrangian cobordisms to a DGA category.With this functorality, an immersed filling $L$ together with an augmentation $\alpha$ of $L$  induce an augmentation of the top Legendrian knot.