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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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
10 July 2025
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| In: |
Mathematische Annalen
Year: 2025, Volume: 392, Issue: 4, Pages: 5209-5233 |
| ISSN: | 1432-1807 |
| DOI: | 10.1007/s00208-025-03212-8 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1007/s00208-025-03212-8
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| Author Notes: | Johanna Bimmermann, Levin Maier |
| Summary: | 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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| Item Description: | Gesehen am 17.11.2025 |
| Physical Description: | Online Resource |
| ISSN: | 1432-1807 |
| DOI: | 10.1007/s00208-025-03212-8 |