AI 中文总结
该研究针对闭辛非球面流形，引入带帽装饰的Floer持续模，证明其层的函子性与稳定性，构造通用帽轮廓伪距离，得到哈密顿共轭类新不变量，可检测普通Floer方法无法察觉的辛映射类位移现象。
AI 中文摘要
对于闭的辛非球面流形，我们通过用齐次上同调理想的迭代作用定义的层来细化作用过滤的哈密顿Floer持续模，引入了带帽装饰的Floer持续。我们证明了这些层的函子性和稳定性，并构造了一个通用的帽轮廓伪距离，其上界由Hofer距离给出。作为应用，我们得到了哈密顿共轭类的新不变量，可检测普通Floer条形码和谱不变量无法察觉的辛映射类位移现象。特别地，对于亏格为2的曲面，我们构造了具有相同普通Floer数据但在哈密顿共轭商中存在正分离的哈密顿微分同胚。
英文摘要
For a closed symplectically aspherical manifold, we introduce cap-decorated Floer persistence by refining the action-filtered Hamiltonian Floer persistence module with layers defined by iterated actions of homogeneous cohomology ideals. We prove functoriality and stability of these layers, and construct a universal cap-profile pseudodistance bounded above by Hofer distance. As an application, we obtain new invariants of Hamiltonian conjugacy classes, detecting symplectic mapping-class displacement phenomena invisible to ordinary Floer barcodes and spectral invariants. In particular, for a genus-two surface we construct Hamiltonian diffeomorphisms with identical ordinary Floer data but positive separation in the Hamiltonian-conjugacy quotient.
Comments45 pages; Comments are very welcome
