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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.10377 |
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| _version_ | 1866913502171496448 |
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| author | Abouzaid, Mohammed Bottman, Nathaniel Niu, Yunpeng |
| author_facet | Abouzaid, Mohammed Bottman, Nathaniel Niu, Yunpeng |
| contents | For a symplectic 4-manifold $M$ equipped with a singular Lagrangian fibration with a section, the natural fiberwise addition given by the local Hamiltonian flow is well-defined on the regular points. We prove, in the case that the singularities are of focus-focus type, that the closure of the corresponding addition graph is the image of a Lagrangian immersion in $(M \times M)^- \times M$, and we study its geometry. Our main motivation for this result is the construction of a symmetric monoidal structure on the Fukaya category of such a manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10377 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The focus-focus addition graph is immersed Abouzaid, Mohammed Bottman, Nathaniel Niu, Yunpeng Symplectic Geometry For a symplectic 4-manifold $M$ equipped with a singular Lagrangian fibration with a section, the natural fiberwise addition given by the local Hamiltonian flow is well-defined on the regular points. We prove, in the case that the singularities are of focus-focus type, that the closure of the corresponding addition graph is the image of a Lagrangian immersion in $(M \times M)^- \times M$, and we study its geometry. Our main motivation for this result is the construction of a symmetric monoidal structure on the Fukaya category of such a manifold. |
| title | The focus-focus addition graph is immersed |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2409.10377 |