Calabi-Yau structures on topological Fukaya categories
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2016
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| _version_ | 1866929343535513600 |
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| author | Shende, Vivek Takeda, Alex |
| author_facet | Shende, Vivek Takeda, Alex |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1605_02721 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Calabi-Yau structures on topological Fukaya categories Shende, Vivek Takeda, Alex Algebraic Geometry Symplectic Geometry 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. |
| title | Calabi-Yau structures on topological Fukaya categories |
| topic | Algebraic Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/1605.02721 |