Band surgery is an operation relating pairs of knots or links in the three‐sphere. We prove that if two quasi‐alternating knots $K$ and $K^{\prime }$ of the same square‐free determinant are related by a band surgery, then the absolute value of the difference in their signatures is either 0 or 8. This obstruction follows from a more general theorem about the difference in the Heegaard Floer $d$‐invariants for pairs of L‐spaces that are related by distance one Dehn fillings and satisfy a certain condition in first homology. These results imply that $T(2,5)$ is the only torus knot $T(2,m)$ with $m$ square‐free that admits a chirally cosmetic banding, that is, a band surgery operation to its mirror image. We conclude with a discussion on the scarcity of chirally cosmetic bandings.

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关于乐队手术和打结的笔记

带外科手术是指在三个球体中成对的结或链接。我们证明如果有两个准交替的结$ķ$ 和 ${ķ}^{\prime }$ 无平方行列式的一个定理通过带手术进行关联，则其签名差异的绝对值为0或8。这种障碍来自关于Heegaard Floer差异的更一般的定理 $d$一对L空间的不变量，它们与一个Dehn填充物的距离相关并且在第一同源性中满足特定条件。这些结果表明$Ť（2，5）$ 是唯一的圆环结 $Ť（2，米）$ 与 $米$无平方的，允许手性装饰带，即对其镜像进行带状手术。最后，我们讨论了手性化妆品条带的稀缺性。