We define several equivariant concordance invariants using knot Floer homology. We show that our invariants provide a lower bound for the equivariant slice genus and use this to give a family of strongly invertible slice knots whose equivariant slice genus grows arbitrarily large, answering a question of Boyle and Issa. We also apply our formalism to several seemingly nonequivariant questions. In particular, we show that knot Floer homology can be used to detect exotic pairs of slice disks, recovering an example due to Hayden, and extend a result due to Miller and Powell regarding stabilization distance. Our formalism suggests a possible route toward establishing the noncommutativity of the equivariant concordance group.

中文翻译：

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等变结和弗洛尔结同源性

我们使用结弗洛尔同源性定义了几个等变一致性不变量。我们证明，我们的不变量为等变切片属提供了下界，并使用它给出了一系列强可逆切片结，其等变切片属增长任意大，回答了博伊尔和伊萨的问题。我们还将形式主义应用于几个看似不等价的问题。特别是，我们证明了结弗洛尔同源性可用于检测奇异的片盘对，恢复海登的例子，并扩展米勒和鲍威尔关于稳定距离的结果。我们的形式主义提出了一条建立等变协调群的非交换性的可能途径。