We prove some necessary conditions for a link to be either concordant to a quasi-positive link, quasi-positive, positive or the closure of a positive braid. The main applications of our results are a characterisation of positive links with unlinking numbers 1 and 2, and a combinatorial criterion to test if a positive link is the closure of a positive braid. Finally, we compile a table of all positive and positive-braid prime links with less than 8 crossings.

中文翻译：

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Slice-torus 链接不变量、组合不变量和正性条件

我们证明了链接与准正链接、准正链接、正链接或正编织的闭合一致的一些必要条件。我们的结果的主要应用是用未链接的数字 1 和 2 表征正链接，以及测试正链接是否是正编织物的闭合的组合标准。最后，我们编制了一个包含少于 8 个交叉点的所有正和正编织素链接的表格。