Completeness of derived interleaving distances and sheaf quantization of non-smooth objects
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866910364886630400 |
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| author | Asano, Tomohiro Ike, Yuichi |
| author_facet | Asano, Tomohiro Ike, Yuichi |
| contents | We develop sheaf-theoretic methods to deal with non-smooth objects in symplectic geometry. We show the completeness of a derived category of sheaves with respect to the interleaving distance and construct a sheaf quantization of a Hamiltonian homeomorphism. We also develop Lusternik--Schnirelmann theory in the microlocal theory of sheaves. With these new sheaf-theoretic methods, we prove an Arnold-type theorem for the image of a compact exact Lagrangian submanifold under a Hamiltonian homeomorphism. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2201_02598 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Completeness of derived interleaving distances and sheaf quantization of non-smooth objects Asano, Tomohiro Ike, Yuichi Symplectic Geometry Algebraic Topology 37J12, 55N31, 18G80, 35A27 We develop sheaf-theoretic methods to deal with non-smooth objects in symplectic geometry. We show the completeness of a derived category of sheaves with respect to the interleaving distance and construct a sheaf quantization of a Hamiltonian homeomorphism. We also develop Lusternik--Schnirelmann theory in the microlocal theory of sheaves. With these new sheaf-theoretic methods, we prove an Arnold-type theorem for the image of a compact exact Lagrangian submanifold under a Hamiltonian homeomorphism. |
| title | Completeness of derived interleaving distances and sheaf quantization of non-smooth objects |
| topic | Symplectic Geometry Algebraic Topology 37J12, 55N31, 18G80, 35A27 |
| url | https://arxiv.org/abs/2201.02598 |