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Title:
On the Hochschild (co)homology of the Fukaya Category
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Abstract:
Let M be an exact symplectic manifold. Under a non-degeneracy assumption implying the existence of enough Lagrangians, we prove that the symplectic cohomology of M is isomorphic to both the Hochschild cohomology and Hochschild homology (with a shift) of M's wrapped Fukaya category. The relevant ingredients are: Fourier-Mukai theory for the wrapped Fukaya category via holomorphic quilts, a version of the Cardy condition, and a new self-duality for the wrapped Fukaya category (a non-compact version of a Calabi-Yau structure).
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