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We prove a twisted Poincaré duality for (full) Hopf algebroids with bijective antipode.As an application, we recover the Hochschild twisted Poincaré duality of van den Bergh.We also get a Poisson twisted Poincaré duality, which was already stated for oriented Poisson manifolds by Chen et al.
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Sophie Chemla (2024) studied this question.
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