Hebrew University topology and geometry seminar

Abstract: To an exact symplectic manifold M, one can associate two important Floer-theoretic invariants: symplectic cohomology SH^*(M), a version of Hamiltonian Floer homology, and the wrapped Fukaya category W(M), a version of the Fukaya category allowing non-compact Lagrangians. We will introduce these invariants along with their mirror symmetry context and study maps between them, which naturally leads to the algebraic construction of Hochschild (co)homology. We will then explain how, when M contains enough Lagrangians, the natural geometric open-closed string maps between the Hochschild homology of W(M), SH^*(M), and the Hochschild cohomology of W(M) are all isomorphisms.