Abstract
We study symplectic invariants of the open symplectic manifolds obtained by plumbing cotangent bundles of 2–spheres according to a plumbing tree . For any tree , we calculate (DG) algebra models of the Fukaya category of closed exact Lagrangians in and the wrapped Fukaya category . When is a Dynkin tree of type or (and conjecturally also for ), we prove that these models for the Fukaya category and are related by (derived) Koszul duality. As an application, we give explicit computations of symplectic cohomology of for , based on the Legendrian surgery formula of Bourgeois, Ekholm and Eliashberg.
Citation
Tolga Etgü. Yankı Lekili. "Koszul duality patterns in Floer theory." Geom. Topol. 21 (6) 3313 - 3389, 2017. https://doi.org/10.2140/gt.2017.21.3313
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