Magnetic billiards and the Hofer-Zehnder capacity of disk tangent bundles of lens spaces
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909716927479808 |
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| author | Bimmermann, Johanna Maier, Levin |
| author_facet | Bimmermann, Johanna Maier, Levin |
| contents | We compute the Hofer-Zehnder capacity of disk tangent bundles of certain lens spaces with respect to the round metric. Interestingly we find that the Hofer-Zehnder capacity does not see the covering, i.e. the capacity of the disk tangent bundle of the lens space coincides with the capacity of the disk tangent bundle of the 3-sphere covering it. In particular, this gives a first example, where Gromov width and Hofer-Zehnder capacity of a disk tangent bundle disagree. Techniques we use include for the lower bound magnetic billiards and for the upper bound Gromov-Witten invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06761 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Magnetic billiards and the Hofer-Zehnder capacity of disk tangent bundles of lens spaces Bimmermann, Johanna Maier, Levin Symplectic Geometry Dynamical Systems We compute the Hofer-Zehnder capacity of disk tangent bundles of certain lens spaces with respect to the round metric. Interestingly we find that the Hofer-Zehnder capacity does not see the covering, i.e. the capacity of the disk tangent bundle of the lens space coincides with the capacity of the disk tangent bundle of the 3-sphere covering it. In particular, this gives a first example, where Gromov width and Hofer-Zehnder capacity of a disk tangent bundle disagree. Techniques we use include for the lower bound magnetic billiards and for the upper bound Gromov-Witten invariants. |
| title | Magnetic billiards and the Hofer-Zehnder capacity of disk tangent bundles of lens spaces |
| topic | Symplectic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2403.06761 |