Koszul duality patterns in Floer theory

2015/02/28 by Tolga Etgü, Yanki Lekili · 2 citations
Mathematics · #math.SG #math.RT

paper · pdf · doi:10.2140/gt.2017.21.3313

published as Geom. Topol. 21 (2017) 3313-3389 · 72 pages, 20 figures/tables. Minor corrections and improvements. To appear in Geometry & Topology

arxiv created 2017/08/28 · arxiv updated 2018/03/16

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 A_n or D_n (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=A_n,D_n, based on the Legendrian surgery formula of Bourgeois, Ekholm and Eliashberg.

Cited by

• Fukaya categories of plumbings and multiplicative preprojective algebras
• Proper modules over Ginzburg dg algebras and compact Fukaya categories of plumbings

Related

• Lagrangian Floer theory, from geometry to algebra and back again
• Hochschild cohomology of the Fukaya category via Floer cohomology with coefficients
• Floer homology in symplectic geometry and in mirror symmetry
• The symplectic geometry of cotangent bundles from a categorical viewpoint
• Functoriality in categorical symplectic geometry