We give a formula for the Heegaard Floer $d$-invariants of integral surgeries on two-component L--space links of linking number zero in terms of the $h$-function, generalizing a formula of Ni and Wu. As a consequence, we characterize L-space surgery slopes for such links in terms of the $\tau$-invariant when the components are unknotted. For general links of linking number zero, we explicitly describe the relationship between the $h$-function, the Sato-Levine invariant and the Casson invariant. We give a proof of a folk result that the $d$-invariant of any nonzero rational surgery on a link of any number of components is a concordance invariant of links in the three-sphere with pairwise linking numbers zero. We also describe bounds on the smooth four-genus of links in terms of the $h$-function, expanding on previous work of the second author, and use these bounds to calculate the four-genus in several examples of links.

中文翻译：

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链接数字 0 和 Heegaard Floer $d$-invariant 的链接的手术

我们给出了Heegaard Floer $d$-不变量在二元L-空间链接上用$h$-函数连接数字0的积分手术的公式，概括了Ni和Wu的公式。因此，当组件未打结时，我们根据 $\tau$-不变量来表征此类链接的 L 空间手术斜率。对于链接数字 0 的一般链接，我们明确描述了 $h$-函数、Sato-Levine 不变量和 Casson 不变量之间的关系。我们给出了一个民间结果的证明，即对任意数量组件的链接进行的任何非零理性手术的 $d$ 不变量是三球中成对链接数为零的链接的一致性不变量。我们还根据 $h$ 函数描述了平滑四类链接的边界，扩展了第二作者以前的工作，