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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.04277 |
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| _version_ | 1866914323616497664 |
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| author | Sun, Yuhan Uljarevic, Igor Varolgunes, Umut |
| author_facet | Sun, Yuhan Uljarevic, Igor Varolgunes, Umut |
| contents | We prove contact big fiber theorems, analogous to the symplectic big fiber theorem by Entov and Polterovich, using symplectic cohomology with support. Unlike in the symplectic case, the validity of the statements requires conditions on the closed contact manifold. One such condition is to admit a Liouville filling with non-zero symplectic cohomology. In the case of Boothby-Wang contact manifolds, we prove the result under the condition that the Euler class of the circle bundle, which is the negative of an integral lift of the symplectic class, is not an invertible element in the quantum cohomology of the base symplectic manifold. As applications, we obtain new examples of rigidity of intersections in contact manifolds and also of contact non-squeezing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Contact big fiber theorems Sun, Yuhan Uljarevic, Igor Varolgunes, Umut Symplectic Geometry We prove contact big fiber theorems, analogous to the symplectic big fiber theorem by Entov and Polterovich, using symplectic cohomology with support. Unlike in the symplectic case, the validity of the statements requires conditions on the closed contact manifold. One such condition is to admit a Liouville filling with non-zero symplectic cohomology. In the case of Boothby-Wang contact manifolds, we prove the result under the condition that the Euler class of the circle bundle, which is the negative of an integral lift of the symplectic class, is not an invertible element in the quantum cohomology of the base symplectic manifold. As applications, we obtain new examples of rigidity of intersections in contact manifolds and also of contact non-squeezing. |
| title | Contact big fiber theorems |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2503.04277 |