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arXiv · 2403.06761

Magnetic billiards and the Hofer-Zehnder capacity of disk tangent bundles of lens spaces

Johanna Bimmermann·Levin Maier
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Abstract

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.

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Johanna Bimmermann, Levin Maier. 2024-03-11. Magnetic billiards and the Hofer-Zehnder capacity of disk tangent bundles of lens spaces. https://doi.org/10.1007/s00208-025-03212-8

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