Augmentation categories in higher dimensions

Abstract

For an exact symplectic manifold $M$ and a Legendrian submanifold $\hat{I}›$ of the contactification $M\times \mathbb{R}$, we construct the augmentation category (over a field of characteristic 2), a unital $A_{\infty }$-category whose objects are augmentations of the Chekanov-Eliashberg differential graded algebra. This extends the construction of the augmentation category by Ng-Rutherford-Shende-Sivek-Zaslow to contact manifolds of dimension greater than 3.

25 pages, minor revision