Invariants of Legendrian Isotopies as Communication of Geometry and Algebra

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• Filip Strakos, Uppsala University
• Friday 16 June 2023, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Macarena Arenas.

The study of Legendrian isotopy classes, in particular contact manifolds, led to defining Chekanov-Eliashberg differential graded algebra, which arises from a relative symplectic field theory. Even though this invariant of Legendrian isotopy is very powerful, it is a daunting task to compute it in general. To obtain a computable invariant, the differential can be augmented using graded augmentations of our DGA (in some cases). We will describe how exact Lagrangian fillings correspond to certain augmentations and how Lagrangian isotopies are carried over to the algebraic setting. If time permits, we will see how deformed Poincare duality and the effect of ambient Legendrian surgery on bilinearized Legendrian contact homology can be used to obtain a DGA -homotopy criterion for augmentations.

This talk is part of the Junior Geometry Seminar series.

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