糖果派对

Speaker: Wenyuan Li
 (University of Southern California) 

Abstract:
Consider sheaves on manifolds with microsupport on a singular Legendrian subset inside the cosphere bundle, which are in particular (real) constructible sheaves. By microlocalization, one can define a sheaf of categories on the singular Legendrian in the cophere bundle, called microsheaves. We will show that the microlocalization functor from sheaves to microsheaves together with its left adjoint admits a strong smooth relative Calabi-Yau structure. This is a non-commutative analogue of the orientation class which induces the Poincare-Lefschetz duality on manifolds with boundary. Under some extra assumptions, we can show that the adjunction is a spherical adjunction. We will explain the connections to Fukaya categories and Legendrian contact homologies. This is joint work with Chris Kuo.