We prove that a version of the Thurston–Bennequin inequality holds for Legendrian and transverse links in a rational homology contact 3-sphere [Formula: see text], whenever [Formula: see text] is tight. More specifically, we show that the self-linking number of a transverse link [Formula: see text] in [Formula: see text], such that the boundary of its tubular neighborhood consists of incompressible tori, is bounded by the Thurston norm [Formula: see text] of [Formula: see text]. A similar inequality is given for Legendrian links by using the notions of positive and negative transverse push-off.We apply this bound to compute the tau-invariant for every strongly quasi-positive link in [Formula: see text]. This is done by proving that our inequality is sharp for this family of smooth links. Moreover, we use a stronger Bennequin inequality, for links in the tight 3-sphere, to generalize this result to quasi-positive links and determine their maximal self-linking number.

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关于紧密接触 3 流形链的 Bennequin 型不等式

我们证明了一个版本的 Thurston-Bennequin 不等式适用于有理同调接触 3 球体 [公式：见文本] 中的 Legendrian 和横向链接，只要 [公式：见文本] 是紧的。更具体地说，我们证明了[公式：见文本]中的横向链接[公式：见文本]的自链接数，使得其管状邻域的边界由不可压缩的环面组成，由瑟斯顿范数[公式：见文本]的[公式：见文本]。通过使用正向和负向横向推离的概念，为 Legendrian 链接给出了类似的不等式。我们应用这个界来计算 [公式：见文本]中每个强准正链接的 tau 不变量。这是通过证明我们的不平等对于这一系列平滑链接来说是尖锐的。此外，我们使用更强的 Bennequin 不等式，