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SUMMARY:Invariants of Legendrian Isotopies as Communication of Geometry an
 d Algebra - Filip Strakos\, Uppsala University
DTSTART:20230616T150000Z
DTEND:20230616T160000Z
UID:TALK198559@talks.cam.ac.uk
CONTACT:Macarena Arenas
DESCRIPTION:The study of Legendrian isotopy classes\, in particular contac
 t manifolds\, led to defining Chekanov-Eliashberg differential graded alge
 bra\, which arises from a relative symplectic field theory. Even though th
 is invariant of Legendrian isotopy is very powerful\, it is a daunting tas
 k to compute it in general. To obtain a computable invariant\, the differe
 ntial can be augmented using graded augmentations of our DGA (in some case
 s). We will describe how exact Lagrangian fillings correspond to certain a
 ugmentations and how Lagrangian isotopies are carried over to the algebrai
 c setting. If time permits\, we will see how deformed Poincare duality and
  the effect of ambient Legendrian surgery on bilinearized Legendrian conta
 ct homology can be used to obtain a DGA-homotopy criterion for augmentatio
 ns.
LOCATION:MR13
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