School of Mathematical Sciences

Koszul duality patterns in Floer theory menu

Koszul duality patterns in Floer theory

Yankı Lekili (King's)
Mon, 22/02/2016 - 16:30
Seminar series: 

Abstract: We study symplectic invariants of the open symplectic manifolds X_Γ obtained by plumbing
cotangent bundles of 2-spheres according to a plumbing tree Γ. For any tree Γ, we calculate
(DG-)algebra models of the Fukaya category F(X_Γ) of closed exact Lagrangians in X_Γ and the
wrapped Fukaya category W(X_Γ). When Γ is a Dynkin tree of type An or Dn (and conjecturally
also for E6 , E7, E8 ), we prove that these models for the Fukaya category F(X_Γ) and W(X_Γ) are
related by (derived) Koszul duality. As an application, we give explicit computations of symplectic
cohomology of X_Γ for Γ = An, Dn , based on the Legendrian surgery formula. In the
case that Γ is non-Dynkin, we merely obtain a spectral sequence that converges to symplectic
cohomology whose E2 -page is given by the Hochschild cohomology of the preprojective algebra
associated to the corresponding Γ. This is joint work with Tolga Etgü.