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

Cyclic homology and S1S1-equivariant symplectic cohomology - Sheel Ganatra

Sheel Ganatra
Stanford University
November 21, 2014
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.