论文标题
在PFH和HF频谱不变性上
On PFH and HF spectral invariants
论文作者
论文摘要
对于闭合的符号表面，有两种类型的光谱不变性：一种由周期性的浮点同源性（PFH）定义，另一种是由定量的Heegaard浮子同源性（QHF）定义的。本文的主题是研究这两个不变的人之间的关系。我们首先使用QHF的圆柱形公式定义中间不变量，我们称之为HF光谱不变性。这些不变性被证明等于作者以前的作品中的链接频谱不变性。在球体的情况下，我们证明该单元的均质HF光谱不变剂等于均质的PFH光谱不变性。该结果是通过构建来自定量Heegaard浮子同源到定期浮点同源性的同态同构来得出的，我们称之为开放式的形态。此外，我们表明均质的PFH光谱不变是准杂形。
For a closed symplectic surface, there are two types of spectral invariants: one defined by periodic Floer homology (PFH) and another by quantitative Heegaard Floer homology (QHF). The theme of this paper is to investigate the relationship between these two invariants. We begin by defining intermediate invariants using the cylindrical formulation of QHF, which we call HF spectral invariants. These invariants are shown to be equivalent to the link spectral invariants in the author's previous work. In the case of the sphere, we prove that the homogenized HF spectral invariants at the unit are equal to the homogenized PFH spectral invariants. This result is derived by constructing homomorphisms from quantitative Heegaard Floer homology to periodic Floer homology, which we refer to as open-closed morphisms. In addition, we show that the homogenized PFH spectral invariants are quasi-morphisms.
