Symplectic topology and ideal-valued measures
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866913279992922112 |
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| author | Dickstein, Adi Ganor, Yaniv Polterovich, Leonid Zapolsky, Frol |
| author_facet | Dickstein, Adi Ganor, Yaniv Polterovich, Leonid Zapolsky, Frol |
| contents | We adapt Gromov's notion of ideal-valued measures to symplectic topology, and use it for proving new results on symplectic rigidity and symplectic intersections. Furthermore, it enables us to discuss three "big fiber theorems", the Centerpoint Theorem in combinatorial geometry, the Maximal Fiber Inequality in topology, and the Non-displaceable Fiber Theorem in symplectic topology, from a unified viewpoint. Our main technical tool is an enhancement of the symplectic cohomology theory recently developed by Varolgunes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_10012 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Symplectic topology and ideal-valued measures Dickstein, Adi Ganor, Yaniv Polterovich, Leonid Zapolsky, Frol Symplectic Geometry Algebraic Topology 53Dxx, 55Uxx We adapt Gromov's notion of ideal-valued measures to symplectic topology, and use it for proving new results on symplectic rigidity and symplectic intersections. Furthermore, it enables us to discuss three "big fiber theorems", the Centerpoint Theorem in combinatorial geometry, the Maximal Fiber Inequality in topology, and the Non-displaceable Fiber Theorem in symplectic topology, from a unified viewpoint. Our main technical tool is an enhancement of the symplectic cohomology theory recently developed by Varolgunes. |
| title | Symplectic topology and ideal-valued measures |
| topic | Symplectic Geometry Algebraic Topology 53Dxx, 55Uxx |
| url | https://arxiv.org/abs/2107.10012 |