On the Hofer-Zehnder capacity for twisted tangent bundles over closed surfaces
| Autor: | Bimmermann, Johanna |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | We determine the Hofer-Zehnder capacity for twisted tangent bundles over closed surfaces for (i) arbitrary constant magnetic fields on the two-sphere and (ii) strong constant magnetic fields for higher genus surfaces. On $S^2$ we further give an explicit $\text{SO}(3)$-equivariant compactification of the twisted tangent bundle to $S^2\times S^2$ with split symplectic form. The former is the phase space of a charged particle moving on the two-sphere in a constant magnetic field, the latter is the configuration space of two massless coupled angular momenta. Comment: The results of this paper are now contained in arXiv:2311.00467 for the part about twisted tangent bundles over surfaces and in paper arXiv:2306.11382 for the part on the symplectomorphism between the twisted tangent bundle of $S^2$ and $S^2\times S^2$ with split symplectic form. The proof presented in arXiv:2311.00467 is very different and much shorter than the proof in this draft |
| Databáze: | arXiv |
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