Abstract categorical residues and Calabi-Yau structures
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916770881732608 |
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| author | Gao, Yuan |
| author_facet | Gao, Yuan |
| contents | Inspired by the simple fact that a compact n-dimensional manifold-with-boundary which satisfies Poincaré-Lefschetz duality of dimension n has a boundary which itself satisfies Poincaré duality of dimension n, we show that the categorical formal punctured neighborhood of infinity, a canonical categorical construction associated to every $A_{\infty}$ category, has a weak proper Calabi-Yau structure of dimension n-1 whenever the original $A_{\infty}$ category admits a weak smooth Calabi-Yau structure of dimension n. Applications include proper Calabi-Yau structures on Rabinowitz Fukaya category of a Liouville manifold and Orlov's singularity category of a proper singular Gorenstein scheme of finite type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05927 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Abstract categorical residues and Calabi-Yau structures Gao, Yuan Symplectic Geometry Algebraic Topology 18G70, 55U30, 53D37 Inspired by the simple fact that a compact n-dimensional manifold-with-boundary which satisfies Poincaré-Lefschetz duality of dimension n has a boundary which itself satisfies Poincaré duality of dimension n, we show that the categorical formal punctured neighborhood of infinity, a canonical categorical construction associated to every $A_{\infty}$ category, has a weak proper Calabi-Yau structure of dimension n-1 whenever the original $A_{\infty}$ category admits a weak smooth Calabi-Yau structure of dimension n. Applications include proper Calabi-Yau structures on Rabinowitz Fukaya category of a Liouville manifold and Orlov's singularity category of a proper singular Gorenstein scheme of finite type. |
| title | Abstract categorical residues and Calabi-Yau structures |
| topic | Symplectic Geometry Algebraic Topology 18G70, 55U30, 53D37 |
| url | https://arxiv.org/abs/2412.05927 |