AI 中文总结
该研究给出分层纽结不变量秩的两个新下界，分别对应纤维纽结的纽结弗洛尔同调和辫子闭包的环形霍万诺夫同调，核心技术是确定纤维纽结单值群添加边界Dehn扭转时的同调行为。
AI 中文摘要
我们给出分层纽结不变量秩的两个新下界：其一针对纤维纽结的纽结弗洛尔同调，依据其单值群的分数Dehn扭转系数给出；其二作为推论，针对辫子闭包的环形霍万诺夫同调，依据该辫子的分数Dehn扭转系数给出。证明中最重要的技术部分是，确定纤维纽结的纽结弗洛尔同调在其单值群上添加边界Dehn扭转时，在次最高Alexander分次下的行为。
英文摘要
We give two new lower bounds on the rank of categorified link invariants: one on the link Floer homology of fibered links in terms of the fractional Dehn twist coefficients of their monodromies, and another, as a corollary, on the annular Khovanov homology of braid closures in terms of the fractional Dehn twist coefficient of the braid. The most important technical component of the proof is that we determine the behaviour of the link Floer homology of fibered links under adding boundary Dehn twists to their monodromies in the next to top Alexander grading.
Comments32 pages, 15 figures, comments welcome!
