标题： 扭曲、稳定化和有边界的Floer同调 显示英文标题

标题： Twisting, Stabilization and Bordered Floer homology

摘要： 考虑一个纽结$c$在$S^3$中和一个纽结$K$在${S^3-N(c)}$中。 沿着$c$扭转结$K$，或者等价地在$c$上应用$\frac{1}{m}$-手术，会产生一组结$\{K_m\}_{m \in \mathbb{Z}}$。 我们使用边界弗洛尔同调和浸入曲线不变量理论来证明，对于$|m|\gg0$，$\widehat{\mathrm{HFK}}(K_m)$、$\tau(K_{m})$的总维数以及$K_{m}$的厚度是$m$的线性函数。 此外，我们证明了$K_m$的亚历山大多项式的极值系数和极值纽结弗洛尔同调在$m$趋于无穷时趋于稳定。 这推广了陈、兰伯特-科尔、罗伯茨、范科特和作者在一致扭转族上的结果。 显示英文摘要

摘要： Consider an unknot $c$ in $S^3$ and a knot $K$ in ${S^3-N(c)}$. Twisting the knot $K$ along $c$, or equivalently applying $\frac{1}{m}$-surgery on $c$, produces a family of knots $\{K_m\}_{m \in \mathbb{Z}}$. We use bordered Floer homology and the theory of immersed curve invariants to show that for $|m|\gg0$, total dimension of $\widehat{\mathrm{HFK}}(K_m)$, $\tau(K_{m})$ and thickness of $K_{m}$ are linear functions of $m$. Furthermore, we prove that the extremal coefficients of the Alexander polynomial and extremal knot Floer homologies of $K_m$ stabilize as $m$ goes to infinity. This generalizes results of Chen, Lambert-Cole, Roberts, Van Cott and the author on coherent twist families.