Bilinearized Legendrian Contact Homology

Geometry Seminar
Topic:Bilinearized Legendrian Contact Homology
Speaker:Frederic Bourgeois
Affiliation:Universite Libre Bruxelles
Date:Friday, November 11
Time/Room:1:30pm - 3:00pm/S-101
Video Link:https://video.ias.edu/geometry/bourgeois

Legendrian contact homology (LCH) is a powerful holomorphic curves invariant for Legendrian submanifolds in contact manifolds. It is defined via a differential graded algebra (DGA), but the computation of its homology is often too difficult. Augmentations of this DGA are then used to obtain a linearized complex; its homology is called linearized LCH. In this talk, we show how pairs of augmentations can be used to define a bilinearized version of LCH, which is a refinement of the linearized LCH. These algebraic constructions will be illustrated with geometric interpretations and applications. This is a joint work with Baptiste Chantraine.