Bohr-Sommerfeld profile surgeries and Disk Potentials
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918495025889280 |
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| author | Chanda, Soham |
| author_facet | Chanda, Soham |
| contents | We construct a new surgery type operation by switching between two exact fillings of Legendrians which we call a BSP surgery. In certain cases, this surgery can preserve monotonicity of Lagrangians. We prove a wall-crossing type formula for the change of the disk-potential under surgery with Bohr-Sommerfeld profiles. As an application, we show that Biran's circle-bundle lifts admit a Bohr-Sommerfeld type surgery. We use the wall-crossing theorem about disk-potentials to construct exotic monotone Lagrangian tori in $\bP^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11603 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bohr-Sommerfeld profile surgeries and Disk Potentials Chanda, Soham Symplectic Geometry Geometric Topology 53D12, 53D40 We construct a new surgery type operation by switching between two exact fillings of Legendrians which we call a BSP surgery. In certain cases, this surgery can preserve monotonicity of Lagrangians. We prove a wall-crossing type formula for the change of the disk-potential under surgery with Bohr-Sommerfeld profiles. As an application, we show that Biran's circle-bundle lifts admit a Bohr-Sommerfeld type surgery. We use the wall-crossing theorem about disk-potentials to construct exotic monotone Lagrangian tori in $\bP^n$. |
| title | Bohr-Sommerfeld profile surgeries and Disk Potentials |
| topic | Symplectic Geometry Geometric Topology 53D12, 53D40 |
| url | https://arxiv.org/abs/2409.11603 |