AI 中文总结
研究 Hirzebruch 曲面中可见拉格朗日量的性质，通过新的展开构造证明其包含拉格朗日环面和克莱因瓶，且其拓扑不由矩映射像决定。
AI 中文摘要
每个偶辛 Hirzebruch 曲面都包含一个拉格朗日环面，每个奇辛 Hirzebruch 曲面都包含一个拉格朗日克莱因瓶作为它们各自的实轨迹。从环面观点看，这是一个可见拉格朗日量，在矩映射下满射到整个矩多面体。本文证明每个 Hirzebruch 曲面都包含具有此性质的拉格朗日环面和拉格朗日克莱因瓶。有趣的是，可见拉格朗日子流形的拓扑不由其在矩映射下的像决定。证明基于一种新构造，即一族哈密顿微分同胚的展开。
英文摘要
Every even symplectic Hirzebruch surface contains a Lagrangian torus and every odd symplectic Hirzebruch surface contains a Lagrangian Klein bottle as their respective real locus. From a toric point of view, this is a visible Lagrangian which surjects to the full moment polytope under the moment map. In this paper, we prove that every Hirzebruch surface contains both a Lagrangian torus and a Lagrangian Klein bottle with this property. An interesting consequence is that the topology of visible Lagrangian submanifolds is not determined by their image under the moment map. The proof is based on a new construction, which we call the spread of a family of Hamiltonian diffeomorphisms.
Comments21 pages, 5 figures, 1 table, minor changes
