The $\gamma $-support as a micro-support
We prove that for any element $L$ in the completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle equipped with the spectral distance, the $\gamma $-support of $L$ coincides with the reduced micro-support of its sheaf quantization. As an application, we give a ch...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-10-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.499/ |
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| Summary: | We prove that for any element $L$ in the completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle equipped with the spectral distance, the $\gamma $-support of $L$ coincides with the reduced micro-support of its sheaf quantization. As an application, we give a characterization of the Vichery subdifferential in terms of $\gamma $-support. |
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| ISSN: | 1778-3569 |