We study global transverse Poincaré sections and give topological obstructions to their existence. We prove that any energy hypersurface equipped with a global transverse Poincaré section has an induced cosymplectic structure. We give a family of Hamiltonian systems with global Poincaré sections of all possible topologies. Finally, we address the question of when a compact hypersurface of a symplectic manifold possesses an induced cosymplectic structure.

中文翻译：

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全球横向庞加莱截面不存在

我们研究了全局庞加莱横截面，并给出了其存在的拓扑障碍。我们证明，配备有整体横向庞加莱截面的任何能量超表面都具有感应的共辛结构。我们为哈密顿系统提供了一个家庭，其中包含所有可能拓扑的全局庞加莱部分。最后，我们解决了辛流形的紧凑超曲面何时具有诱导的共辛结构的问题。