Augmentation categories in higher dimensions

Abstract: For an exact symplectic manifold (M) and a Legendrian submanifold (\Lambda) 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. This paper is a step in generalising the ``augmentations are sheaves'' result of Ng-Rutherford-Shende-Sivek-Zaslow to all 1-jet spaces.