Periodic Symplectic Cohomologies

Jingyu Zhao

Periodic cyclic homology group associated to a mixed complex was introduced by Goodwillie. In this talk, I will explain how to apply this construction to the symplectic cochain complex of a Liouville domain and obtain two periodic symplectic cohomology theories, which are called periodic symplectic cohomology and finitely supported periodic symplectic cohomology, respectively. The main result is that there is a localization theorem for the finitely supported periodic symplectic cohomology.

http://scgp.stonybrook.edu/video_portal/video.php?id=1591

Simons- Program: Moduli Spaces of Pseudo-holomorphic curves and their applications to Symplectic Topology