The derived equivalence conjecture for the compactified Fukaya category
The derived equivalence conjecture for the compactified Fukaya category
Let be an exact symplectic manifold embedded in a closed symplectic manifold as in Assumption. Let be the generic fibre of the -deformation of the Fukaya category, and let be the Novikov ring. Derived equivalence conjecture. There is a canonical equivalence of triangulated categories
This predicts that, after passing to derived categories and extending scalars, the generic fibre built from Lagrangians lying in recovers the Fukaya category of the closed manifold ; the source indicates that the deformation construction itself has not yet been fully carried out.
Sources & referencesView supporting material
Primary source
Paul Seidel, “Fukaya categories and deformations”, arXiv:math/0206155 (2002).
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