Michael Sullivan: Cellular homology, augmentations and generating families for Legendrian surfaces

Given a Legendrian surface in a contact one jet space, there is a local combinatorial DGA associated to the cell decomposition of the base projection of the Legendrian. The DGA is quasi-isomorphic to the Legendrian contact DGA. Using this reformulation I show how a generating family for the Legendrian  produces an augmentation for the DGA. I will also sketch a partial converse. This is joint work with Dan Rutherford.