Augmentations and immersed Lagrangian fillings

Abstract: The Legendrian contact DGA (differential graded algebra) is a fundamental invariant of Legendrian submanifolds that is functorial for a class of Lagrangian cobordisms. In particular, a Lagrangian filling of a Legendrian knot induces an augmentation, i.e. a DGA map $\mathcal{A}(\Lambda)\to \mathbb{F}$ to a base field. It is natural to ask: Can every augmentation be induced by a Lagrangian filling?. The answer is no, and we will survey known obstructions to inducing augmentations by fillings and give some new examples (joint with H. Gao) of non-fillable augmentations of Legendrian twist knots. We will then present a complementary result (joint with Y. Pan) showing that any augmentation can in fact be induced by an immersed Lagrangian filling. Time permitting we will discuss (joint work in progress with H. Gao) examples of immersed fillings related to ruling stratifications of augmentation varieties.

algebraic geometry

Audience: researchers in the topic

UC Davis algebraic geometry seminar