Morse-Novikov理论与Floer理论的抽象层间持续性
Abstract interlevel persistence for Morse-Novikov and Floer theory
AI总结：
本研究构建含庞加莱-诺维科夫结构与滤过匹配对的通用代数框架，为Morse函数层间集同调条形码提供抽象方法，可推广至Floer理论，所得条形码满足稳定性与对偶性，在哈密顿Floer理论中可导出类谱范数量。
摘要：
我们构建了包含“庞加莱-诺维科夫结构”与“滤过匹配对”的通用代数框架，为取值于$\boldsymbol{\rm \text{或}}$的Morse函数的层间集同调对应的条形码提供抽象方法，该方法可应用于无明显层间集类似物的Floer理论场景。所得条形码满足抽象版本的稳定性与对偶定理，在Morse或Novikov理论中，其与层间持续性产生的标准条形码完全一致。在哈密顿Floer理论中，条带的长度可导出多个与哈密顿微分同胚的谱范数相似的量。
英文摘要：
We develop a general algebraic framework involving "Poincaré--Novikov structures" and "filtered matched pairs" to provide an abstract approach to the barcodes associated to the homologies of interlevel sets of $\mathbb{R}$- or $S^1$-valued Morse functions, which can then be applied to Floer-theoretic situations where no readily apparent analogue of an interlevel set is available. The resulting barcodes satisfy abstract versions of stability and duality theorems, and in the case of Morse or Novikov theory they coincide with the standard barcodes coming from interlevel persistence. In the case of Hamiltonian Floer theory, the lengths of the bars yield multiple quantities that are reminiscent of the spectral norm of a Hamiltonian diffeomorphism.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
