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

Autor:	Bimmermann, Johanna, Maier, Levin
Rok vydání:	2024
Předmět:	Mathematics - Symplectic Geometry Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	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. Comment: 23 pages, 5 figures. Comments are welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.06761 Zobrazit plný text záznamu View this record from Arxiv