In this paper, we prove that the Ozsv\'ath-Szab\'o invariant of a contact 3-manifold vanishes if it can be obtained by contact $+1$ surgery on the standard contact 3-sphere along a Legendrian two-component link whose linking number is nonzero and the topological type of one of whose components is smoothly slice. As a corollary, the Ozsv\'ath-Szab\'o invariant of a contact $\frac{1}{n}$ surgery on the standard tight $\sharp^{k}(S^{1}\times S^{2})$ along a homologically essential Legendrian knot vanishes for any positive integer $n$. As another corollary, the contact $+1$ surgery along a Legendrian two-component link is not strongly symplectic fillable whenever the linking number is nonzero. In addition, we give a sufficient condition for the contact $+1$ surgery on the standard contact 3-sphere along a Legendrian two-component link being overtwisted.

中文翻译：

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接触 (+1) - 沿勒让德二元链接的手术

在本文中，我们证明了接触 3-流形的 Ozsv\'ath-Szab\'o 不变量如果可以通过对标准接触 3-球体沿勒让德二分量进行接触 $+1$ 手术获得链接数为非零且其组件之一的拓扑类型为平滑切片的链接。作为推论，接触 $\frac{1}{n}$ 手术的 Ozsv\'ath-Szab\'o 不变量对标准紧 $\sharp^{k}(S^{1}\times S^ {2})$ 沿着一个同源本质的勒让德结消失对于任何正整数 $n$。作为另一个推论，当链接数非零时，沿勒让德双分量链接的接触 $+1$ 手术不是强辛可填充的。此外，