GT Seminar: DGA-homotopy criteria for augmentations of CE-algebras

Abstract: In a suitably generic situation the differential of Chekanov-Eliashberg algebra can be augmented. The set of all DGA-homotopy classes of augmentations is then a Legendrian isotopy invariant, and so is its cardinality. We will use linearized and bilinearized Legendrian contact homology to derive DGA-homotopy criteria for connected and disconnected Legendrian submanifolds respectively. In particular, we will see that while in the connected case the DGA-homotopy criterion descends to the chain level, this is no longer true in the disconnected case. Then we will apply the results to the question of geography of the bilinearized Legendrian contact homology generalizing results of Bourgeois and Galant.