论文标题
链路浮子同源性和检测结果中的等级界限
Rank Bounds in Link Floer Homology and Detection Results
论文作者
论文摘要
将辫子不变视为链接浮子同源性的生成器，我们概括了鲍德温 - 维拉 - 维克（Baldwin-Vela-Vick）的作品，以在调节浮子同源性的接下来等级上获得等级界限。这些使我们能够将链接与排名最多的链路同源性分类，并证明与Xie-Zhang有关的Khovanov同源性的链接分类。在另一个方向上，我们使用$ e_2 $的ozsváth-szabó分类折叠$ \ mathbb {z} \ oplus \ mathbb {z} $过滤链链复合物，以表明结式浮子同源物检测到$ t（2,8）$ t（2,8）$和$ t（2,10）$。将这些技术与蝙蝠种子，道林和李的光谱序列相结合，我们可以证明Khovanov同源性同样可以检测到$ t（2,8）$和$ t（2,10）$。
Viewing the BRAID invariant as a generator of link Floer homology we generalise work of Baldwin-Vela-Vick to obtain rank bounds on the next to top grading of knot Floer homology. These allow us to classify links with knot Floer homology of rank at most eight, and prove a variant of a classification of links with Khovanov homology of low rank due to Xie-Zhang. In another direction we use a variant of Ozsváth-Szabó classification of $E_2$ collapsed $\mathbb{Z} \oplus\mathbb{Z}$ filtered chain complexes to show that knot Floer homology detects $T(2,8)$ and $T(2,10)$. Combining these techniques with the spectral sequences of Batson-Seed, Dowlin, and Lee we can show that Khovanov homology likewise detects $T(2,8)$ and $T(2,10)$.
