Deformations of asymptotically cylindrical associative submanifolds
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918112662650880 |
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| author | Bera, Gorapada |
| author_facet | Bera, Gorapada |
| contents | This article develops the deformation theory of asymptotically cylindrical (ACyl) associative submanifolds in ACyl $G_2$-manifolds, laying the foundation for the gluing of ACyl associative submanifolds in twisted connected sum $G_2$-manifolds presented by the author in [Ber22]. We study the moduli space of ACyl associative submanifolds with a fixed asymptotic holomorphic curve and a fixed rate, as well as the moduli space where this asymptotic data is allowed to vary, each endowed with a natural topology. We compute their virtual dimensions and show that in the best-case scenario, the latter embeds as a Lagrangian submanifold in the moduli space of holomorphic curves of the limiting Calabi-Yau 3-fold. These results may also be of independent interest for future. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01899 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deformations of asymptotically cylindrical associative submanifolds Bera, Gorapada Differential Geometry This article develops the deformation theory of asymptotically cylindrical (ACyl) associative submanifolds in ACyl $G_2$-manifolds, laying the foundation for the gluing of ACyl associative submanifolds in twisted connected sum $G_2$-manifolds presented by the author in [Ber22]. We study the moduli space of ACyl associative submanifolds with a fixed asymptotic holomorphic curve and a fixed rate, as well as the moduli space where this asymptotic data is allowed to vary, each endowed with a natural topology. We compute their virtual dimensions and show that in the best-case scenario, the latter embeds as a Lagrangian submanifold in the moduli space of holomorphic curves of the limiting Calabi-Yau 3-fold. These results may also be of independent interest for future. |
| title | Deformations of asymptotically cylindrical associative submanifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2508.01899 |