Cohomology in algebra, geometry, physicsand statistics

Augmentations of Chekanov-Eliashberg Algebra and Geography of Bilinearized Legendrian Contact Homology

 We will start with a brief introduction to a relative version of symplectic field theory (SFT) for Legendrian submanifolds in a particular class of contact manifolds. This will provide us with Chekanov-Eliashberg differential graded algebra (DGA), whose homology is an invariant of Legendrian isotopy. This algebraic structure is difficult to compute and so we will simplify the differential using (bi)linearization. Then we will sketch the proof of DGA-homotopy criterion for augmentations using a duality long exact sequence, which may be seen as a version of Poincare duality for this relative SFT. We will mention the geometric origin of those augmentations coming from exact Lagrangian fillings of our Legendrian submanifold. If time permits, we will show the application of the mentioned results to the question of geography for bilinearized Legendrian contact homology of disconnected Legendrian submanifolds in a one jet space, which is a generalization of work of Bourgeois and Galant for the connected case.
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We shall open the ZOOM meeting at 13.15 for virtual coffee. Join Zoom Meeting
 
https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09
 
MeetingID:99598413922
 
Passcode:Galois