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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.03823 |
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| _version_ | 1866909798031687680 |
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| author | Kilgore, Eric |
| author_facet | Kilgore, Eric |
| contents | We show that Legendrian pre-quantization lifts of many non-exact Lagrangian submanifolds in $\mathbb{C}^n$ retain some quantitative rigidity from the symplectic base. In particular, they cannot be moved by Legendrian isotopy into an arbitrarily small pre-quantized cylinder. This is a high dimensional generalization of results of Dimitroglou Rizell--Sullivan in dimension 3. In this setting, we give a new proof of non-squeezing using normal rulings, and in high dimension, we obtain our results using a category of (micro)sheaves associated to a Legendrian submanifold of pre-quantizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03823 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Legendrian non-squeezing via microsheaves Kilgore, Eric Symplectic Geometry We show that Legendrian pre-quantization lifts of many non-exact Lagrangian submanifolds in $\mathbb{C}^n$ retain some quantitative rigidity from the symplectic base. In particular, they cannot be moved by Legendrian isotopy into an arbitrarily small pre-quantized cylinder. This is a high dimensional generalization of results of Dimitroglou Rizell--Sullivan in dimension 3. In this setting, we give a new proof of non-squeezing using normal rulings, and in high dimension, we obtain our results using a category of (micro)sheaves associated to a Legendrian submanifold of pre-quantizations. |
| title | Legendrian non-squeezing via microsheaves |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2412.03823 |