Magnetic billiards and the Hofer-Zehnder capacity of disk tangent bundles of lens spaces
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 d...
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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
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10 July 2025
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| In: |
Mathematische Annalen
Year: 2025, Jahrgang: 392, Heft: 4, Pages: 5209-5233 |
| ISSN: | 1432-1807 |
| DOI: | 10.1007/s00208-025-03212-8 |
| Online-Zugang: | Verlag, kostenfrei, Volltext: https://doi.org/10.1007/s00208-025-03212-8
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| Verfasserangaben: | Johanna Bimmermann, Levin Maier |
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| 520 | |a 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. We use techniques that include magnetic billiards for the lower bound and Gromov-Witten invariants for the upper bound. | ||
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