论文标题
具有接触类型边界的流形的符号圆动作
Symplectic circle actions on manifolds with contact type boundary
论文作者
论文摘要
封闭的汉密尔顿G-manifolds的许多现有结果都是基于使用Morse-Bott技术对相应的Hamiltonian功能的分析。通常，这种方法对于非紧缩歧管或具有边界的歧管失败。 在本文中，我们仅在具有（凸）接触类型边界的符号歧管上考虑圆圈动作。在这种情况下，我们表明，莫尔斯 - 哥特理论的许多关键思想仍然存在，使我们能够从封闭环境中概括一些结果。 其中，我们表明，在我们的情况下，任何符合性的群体行动始终是哈密顿人，我们展示了有关符号歧管的拓扑结构，尤其是关于其边界的联系。我们还表明，连接圆柱末端后，一组圆形动作的哈密顿量为空或连接。 我们主要集中于圆形动作，但我们认为，通过我们的方法，许多经典结果可以从封闭的符号歧管推广到具有接触类型边界的符号歧管。
Many of the existing results for closed Hamiltonian G-manifolds are based on the analysis of the corresponding Hamiltonian functions using Morse-Bott techniques. In general such methods fail for non-compact manifolds or for manifolds with boundary. In this article, we consider circle actions only on symplectic manifolds that have (convex) contact type boundary. In this situation we show that many of the key ideas of Morse-Bott theory still hold, allowing us to generalize several results from the closed setting. Among these, we show that in our situation any symplectic group action is always Hamiltonian, we show several results about the topology of the symplectic manifold and in particular about the connectedness of its boundary. We also show that after attaching cylindrical ends, a level set of the Hamiltonian of a circle action is either empty or connected. We concentrate mostly on circle actions, but we believe that with our methods many of the classical results can be generalized from closed symplectic manifolds to symplectic manifolds with contact type boundary.
