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Fukaya categories and deformations
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This is an informal (and mostly conjectural) discussion of some aspects of Fukaya categories. We start by looking at exact symplectic manifolds which are obtained from a closed Calabi-Yau by removing a hyperplane section. We look at the possible geometric significance of Hochschild cohomology in this situation, and how one can try to get from the Fukaya category of the exact manifold to that of the closed Calabi-Yau. Also included is a brief discussion of the role of Lefschetz pencils, and a bit of general deformation theory. To appear in the Proceedings of the Beijing ICM.
Forward citations
Cited by 2 Pith papers
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A Deformation of the Compact Fukaya Category via the Relative Fukaya Category
The compact subcategory W(M,D) of the CO(β)-deformed wrapped Fukaya category is filtered quasi-equivalent to Seidel's relative Fukaya category F(M,D).
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Fukaya categories of Coulomb branches as unique deformations
Fukaya categories of horizontal Hilbert schemes arise as the unique Z^2-graded deformations of the NilHecke algebra after removing the matter divisor.
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