关于周期Floer同调上的配边映射
几何拓扑
2022-01-24 v3
摘要
本文中，我们研究周期Floer同调(PFH)上的配边映射。在论文第一部分，我们通过Seiberg Witten理论定义PFH上的配边映射以及PFH与Seiberg Witten上同调之间的同构。此外，我们证明这些映射满足全纯曲线公理。在论文第二部分，我们给出这些映射的另一种定义，使用全纯曲线方法，前提是辛配边是满足某些良好条件的Lefschetz纤维化。在附加某些单调性假设下，我们证明这两种定义等价。
引用
@article{arxiv.1709.04270,
title = {On cobordism maps on periodic Floer homology},
author = {Guanheng Chen},
journal= {arXiv preprint arXiv:1709.04270},
year = {2022}
}
备注
The preview title of this paper is "Cobordism Maps on PFH induced by Lefschetz Fibration over Higher Genus Base". According to referees'suggestion, I change it to be "On cobordism maps on periodic Floer homology". In this version, the exposition of the paper is improved. Besides, I correct some mistakes about the composition rule and restate Theorem 1 for a general setting