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arXiv · 1605.02721

Calabi-Yau structures on topological Fukaya categories

Vivek Shende·Alex Takeda
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Abstract

We develop a local-to-global formalism for constructing Calabi-Yau structures for global sections of constructible sheaves or cosheaves of categories. The required data - an isomorphism of the sheafified Hochschild homology with the topological dualizing sheaf - specializes to the classical notion of orientation when applied to the category of local systems on a manifold. We apply this construction to the cosheaves on arboreal skeleta arising in the microlocal approach to the A-model.

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Vivek Shende, Alex Takeda. 2016-05-09. Calabi-Yau structures on topological Fukaya categories. https://arxiv.org/abs/1605.02721

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