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| Main Author: | |
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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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Table of 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.