Regular Lagrangians are smooth Lagrangians
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913800164212736 |
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| author | Asano, Tomohiro Guillermou, Stéphane Ike, Yuichi Viterbo, Claude |
| author_facet | Asano, Tomohiro Guillermou, Stéphane Ike, Yuichi Viterbo, Claude |
| contents | We prove that for any element in the $γ$-completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle, if its $γ$-support is a smooth Lagrangian submanifold, then the element itself is a smooth Lagrangian. We also prove that if the $γ$-support of an element in the completion is compact, then it is connected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00395 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regular Lagrangians are smooth Lagrangians Asano, Tomohiro Guillermou, Stéphane Ike, Yuichi Viterbo, Claude Symplectic Geometry Algebraic Topology Category Theory 53D12, 37J11, 35A27 We prove that for any element in the $γ$-completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle, if its $γ$-support is a smooth Lagrangian submanifold, then the element itself is a smooth Lagrangian. We also prove that if the $γ$-support of an element in the completion is compact, then it is connected. |
| title | Regular Lagrangians are smooth Lagrangians |
| topic | Symplectic Geometry Algebraic Topology Category Theory 53D12, 37J11, 35A27 |
| url | https://arxiv.org/abs/2407.00395 |