Augmentation categories in higher dimensions

Tsinghua-BIMSA

symplectic geometry seminar

Organizers：

Kenji Fukaya, Honghao Gao, Hang Yuan

Speaker：

Hanming Liu (University of Oregon)

Time：

Thur., 2:00-3:00 pm, Sept. 11, 2025

Venue：

C548, Shuangqing Complex Building A

Title：

Augmentation categories in higher dimensions

Abstract:

For a compact Legendrian submanifold of a 1-jet space, one can associate to it the augmentation category, which is a unital A-infinity category, whose objects are the augmentations of the Chekanov-Eliashberg DGA of the Legendrian, and is conjecturally equivalent to the rank 1 microlocal sheaf category. This extends the construction of such a category in the case of Legendrian links in standard contact 3-space by Ng-Rutherford-Shende-Sivek-Zaslow. In this talk, I will sketch the construction of the augmentation category, and if time permits, I will also talk about some work in progress about a partially wrapped version of contact Fukaya category in 1-jet spaces.