Moduli of special Lagrangians with boundary, I: Unobstructed Deformations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913788166406144 |
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| author | Pidaparthy, Vasanth |
| author_facet | Pidaparthy, Vasanth |
| contents | This article studies the deformation problem for compact special Lagrangians with boundary in a Calabi--Yau manifold, with each boundary component constrained along a given Lagrangian submanifold. The tangent vectors generating such deformations are identified with harmonic 1-forms vanishing on the boundary of the special Lagrangian, and the deformation generated by any such tangent vector is unobstructed. Consequently, the moduli space of special Lagrangians with boundary is a smooth manifold whose dimension equals the dimension of the first relative cohomology of the special Lagrangian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23525 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moduli of special Lagrangians with boundary, I: Unobstructed Deformations Pidaparthy, Vasanth Differential Geometry This article studies the deformation problem for compact special Lagrangians with boundary in a Calabi--Yau manifold, with each boundary component constrained along a given Lagrangian submanifold. The tangent vectors generating such deformations are identified with harmonic 1-forms vanishing on the boundary of the special Lagrangian, and the deformation generated by any such tangent vector is unobstructed. Consequently, the moduli space of special Lagrangians with boundary is a smooth manifold whose dimension equals the dimension of the first relative cohomology of the special Lagrangian. |
| title | Moduli of special Lagrangians with boundary, I: Unobstructed Deformations |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2503.23525 |