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Shifted symplectic structure on Poisson Lie algebroid and generalized complex geometry
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Generalized complex geometry was classically formulated by the language of differential geometry. In this paper, we reformulated a generalized complex manifold as a holomorphic symplectic differentiable formal stack in a homotopical sense. Meanwhile, by developing the machinery for shifted symplectic formal stack, we prove that the coisotropic intersection inherits shifted Poisson structure. Generalized complex branes are also studied.
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Advancements in Functorial Homological Mirror Symmetry
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