Deformations of Lagrangian $NQ$-submanifolds
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909311014273024 |
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| author | Cueca, Miquel Schnitzer, Jonas |
| author_facet | Cueca, Miquel Schnitzer, Jonas |
| contents | In this paper we prove graded versions of the Darboux Theorem and Weinstein's Lagrangian tubular neighbourhood Theorem in order to study the deformation theory of Lagrangian $NQ$-submanifolds of degree $n$ symplectic $NQ$-manifolds. Using Weinstein's Lagrangian tubular neighbourhood Theorem, we attach to every Lagrangian $NQ$-submanifold an $L_\infty$-algebra, which controls its deformation theory. The main examples are coisotropic submanifolds of Poisson manifolds and (higher) Dirac structures with support in (higher) Courant algebroids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05580 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Deformations of Lagrangian $NQ$-submanifolds Cueca, Miquel Schnitzer, Jonas Symplectic Geometry Mathematical Physics Differential Geometry 58A50, 53D12, 53D18 In this paper we prove graded versions of the Darboux Theorem and Weinstein's Lagrangian tubular neighbourhood Theorem in order to study the deformation theory of Lagrangian $NQ$-submanifolds of degree $n$ symplectic $NQ$-manifolds. Using Weinstein's Lagrangian tubular neighbourhood Theorem, we attach to every Lagrangian $NQ$-submanifold an $L_\infty$-algebra, which controls its deformation theory. The main examples are coisotropic submanifolds of Poisson manifolds and (higher) Dirac structures with support in (higher) Courant algebroids. |
| title | Deformations of Lagrangian $NQ$-submanifolds |
| topic | Symplectic Geometry Mathematical Physics Differential Geometry 58A50, 53D12, 53D18 |
| url | https://arxiv.org/abs/2309.05580 |