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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.16440 |
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| _version_ | 1866911930541670400 |
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| author | Bimmermann, Johanna |
| author_facet | Bimmermann, Johanna |
| contents | We explicitly construct a symplectomorphism that relates magnetic twists to the invariant hyperkähler structure of the tangent bundle of a Hermitian symmetric space. This symplectomorphism reveals foliations by (pseudo-) holomorphic planes, predicted by vanishing of symplectic homology. Furthermore, in the spirit of Weinstein's tubular neighborhood theorem, we extend the (Lagrangian) diagonal embedding of a compact Hermitian symmetric space to an open dense embedding of a specified neighborhood of the zero section. Using this embedding, we compute the Gromov width and Hofer-Zehnder capacity of these neighborhoods of the zero section. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On symplectic geometry of tangent bundles of Hermitian symmetric spaces Bimmermann, Johanna Symplectic Geometry 32M15, 14J42, 53D20 We explicitly construct a symplectomorphism that relates magnetic twists to the invariant hyperkähler structure of the tangent bundle of a Hermitian symmetric space. This symplectomorphism reveals foliations by (pseudo-) holomorphic planes, predicted by vanishing of symplectic homology. Furthermore, in the spirit of Weinstein's tubular neighborhood theorem, we extend the (Lagrangian) diagonal embedding of a compact Hermitian symmetric space to an open dense embedding of a specified neighborhood of the zero section. Using this embedding, we compute the Gromov width and Hofer-Zehnder capacity of these neighborhoods of the zero section. |
| title | On symplectic geometry of tangent bundles of Hermitian symmetric spaces |
| topic | Symplectic Geometry 32M15, 14J42, 53D20 |
| url | https://arxiv.org/abs/2406.16440 |