Cyclic homology and \(S^1\)-equivariant symplectic cohomology

Princeton/IAS Symplectic Geometry Seminar
Topic:Cyclic homology and \(S^1\)-equivariant symplectic cohomology
Speaker:Sheel Ganatra
Affiliation:Stanford University
Date:Friday, November 21
Time/Room:1:30pm - 2:30pm/S-101
Video Link:http://video.ias.edu/pisgs/2014/1121-SheelGanatra

In this talk, we study two natural circle actions in Floer theory, one on symplectic cohomology and one on the Hochschild homology of the Fukaya category. We show that the geometric open-closed string map between these two complexes is \(S^1\)-equivariant, at a suitable chain level. In particular, there are induced maps between equivariant homology theories, natural with respect to Gysin sequences, which are isomorphisms whenever the non-equivariant map is.