Simultaneous Deformations of Symplectic Forms and Lagrangian Submanifolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918263310516224 |
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| author | Geudens, Stephane Schaetz, Florian Tortorella, Alfonso G. |
| author_facet | Geudens, Stephane Schaetz, Florian Tortorella, Alfonso G. |
| contents | Given a compact symplectic manifold $(M,ω)$ and a compact Lagrangian submanifold $L\subset(M,ω)$, we describe small deformations of the pair $(ω,L)$ modulo the action by isotopies. We show that the resulting moduli space can be identified with an open neighborhood of the origin in the second relative de Rham cohomology group $H^2(M,L)$. This implies in particular that the moduli space is smooth and finite dimensional. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_21225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simultaneous Deformations of Symplectic Forms and Lagrangian Submanifolds Geudens, Stephane Schaetz, Florian Tortorella, Alfonso G. Symplectic Geometry Differential Geometry 53D12, 58H15, 58D27, 17B70 Given a compact symplectic manifold $(M,ω)$ and a compact Lagrangian submanifold $L\subset(M,ω)$, we describe small deformations of the pair $(ω,L)$ modulo the action by isotopies. We show that the resulting moduli space can be identified with an open neighborhood of the origin in the second relative de Rham cohomology group $H^2(M,L)$. This implies in particular that the moduli space is smooth and finite dimensional. |
| title | Simultaneous Deformations of Symplectic Forms and Lagrangian Submanifolds |
| topic | Symplectic Geometry Differential Geometry 53D12, 58H15, 58D27, 17B70 |
| url | https://arxiv.org/abs/2512.21225 |