Let $\mathcal{L}$ be a knot with a fixed positive crossing and $\mathcal{L}_n$ the link obtained by replacing this crossing with $n$ positive twists. We prove that the knot Floer homology $\widehat{\text{HFK}}(\mathcal{L}_n)$ `stabilizes' as $n$ goes to infinity. This categorifies a similar stabilization phenomenon of the Alexander polynomial. As an application, we construct an infinite family of prime, positive mutant knots with isomorphic bigraded knot Floer homology groups. Moreover, given any pair of positive mutants, we describe how to derive a corresponding infinite family positive mutants with isomorphic bigraded $\widehat{\text{HFK}}$ groups, Seifert genera, and concordance invariant $\tau$.

中文翻译：

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扭曲、突变和结 Floer 同源性

让 $\mathcal{L}$ 是一个带有固定正交叉的结，$\mathcal{L}_n$ 是通过用 $n$ 正扭曲替换这个交叉而获得的链接。我们证明了结 Floer 同源性 $\widehat{\text{HFK}}(\mathcal{L}_n)$ 随着 $n$ 趋于无穷大而“稳定”。这归类了亚历山大多项式的类似稳定现象。作为一个应用，我们构建了一个具有同构双分级结 Floer 同源群的素数、正突变结的无限族。此外，给定任何一对正突变体，我们描述了如何推导出具有同构双梯度 $\widehat{\text{HFK}}$ 组、Seifert 属和一致性不变量 $\tau$ 的相应无限家族正突变体。