闭曲面上扭曲切丛的 Hofer-Zehnder 容量
辛几何
2023-11-10 v2 微分几何
摘要
我们确定了闭曲面上扭曲切丛的 Hofer-Zehnder 容量，针对（i）二维球面上任意常磁场以及（ii）高亏格曲面上强常磁场的情形。在 上，我们进一步给出了扭曲切丛到具有分裂辛形式的 的显式 -等变紧化。前者是在常磁场中于二维球面上运动的带电粒子的相空间，后者是两个无质量耦合角动量的构型空间。
引用
@article{arxiv.2011.09828,
title = {On the Hofer-Zehnder capacity for twisted tangent bundles over closed surfaces},
author = {Johanna Bimmermann},
journal= {arXiv preprint arXiv:2011.09828},
year = {2023}
}
备注
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