Formality of differential graded algebras and complex Lagrangian submanifolds
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866917388681740288 |
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| author | Mladenov, Borislav |
| author_facet | Mladenov, Borislav |
| contents | Let $i: \mathrm{L} \hookrightarrow \mathrm{X}$ be a compact Kähler Lagrangian in a holomorphic symplectic variety $\mathrm{X}/\mathbf{C}$. We use deformation quantisation to show that the endomorphism differential graded algebra $\mathrm{RHom}\big(i_*\mathrm{K}_\mathrm{L}^{1/2},i_*\mathrm{K}_\mathrm{L}^{1/2}\big)$ is formal. We prove a generalisation to pairs of Lagrangians, along with auxiliary results on the behaviour of formality in families of $\mathrm{A}_\infty$-modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_05498 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Formality of differential graded algebras and complex Lagrangian submanifolds Mladenov, Borislav Algebraic Geometry Quantum Algebra Symplectic Geometry 16E45, 14J42, 53D12, 53D55 (Primary) 18G40, 14F40 (Secondary) Let $i: \mathrm{L} \hookrightarrow \mathrm{X}$ be a compact Kähler Lagrangian in a holomorphic symplectic variety $\mathrm{X}/\mathbf{C}$. We use deformation quantisation to show that the endomorphism differential graded algebra $\mathrm{RHom}\big(i_*\mathrm{K}_\mathrm{L}^{1/2},i_*\mathrm{K}_\mathrm{L}^{1/2}\big)$ is formal. We prove a generalisation to pairs of Lagrangians, along with auxiliary results on the behaviour of formality in families of $\mathrm{A}_\infty$-modules. |
| title | Formality of differential graded algebras and complex Lagrangian submanifolds |
| topic | Algebraic Geometry Quantum Algebra Symplectic Geometry 16E45, 14J42, 53D12, 53D55 (Primary) 18G40, 14F40 (Secondary) |
| url | https://arxiv.org/abs/2007.05498 |