AI 中文总结
本文针对满足特定 Seifert 曲面条件的非纤维纽结，独立推广了 Baldwin 与 Vela-Vick 验证的 Sivek 关于纽结 Floer 同调秩的猜想结果。
AI 中文摘要
Sivek 猜想，在次顶 Alexander 分次下的纽结 Floer 同调秩至少为顶 Alexander 分次下的秩。Baldwin 和 Vela-Vick 在纤维纽结的情形下验证了该猜想（arXiv:1801.06563）。Ni 将该结果推广到满足某一代数条件的广义 L 空间中的纽结情形（arXiv:2104.14687）。我们独立地将 Baldwin 和 Vela-Vick 的结果推广到一族满足特定条件的 Seifert 曲面纽结。
英文摘要
Sivek conjectured that the rank of knot Floer homology in the next-to-top Alexander grading is at least the rank in the top Alexander grading. Baldwin and Vela-Vick verified this conjecture in the case of fibered knots arXiv:1801.06563. Ni gave a generalization of this result (for knots in generalized $L$-spaces) to cases in which the knot Floer homology satisfies an algebraic condition arXiv:2104.14687. We give an independent generalization of Baldwin and Vela-Vick's result to a family of knots with Seifert surfaces satisfying certain conditions.
Comments29 pages, 8 figures, comments welcome
