In [V. O. Manturov, An almost classification of free knots, Dokl. Math. 88(2) (2013) 556–558.] the second author constructed an invariant which in some sense generalizes the quantum [Formula: see text] link invariant of Kuperberg to the case of free links. In this paper, we generalize this construction to free graph-links. As a result, we obtain an invariant of free graph-links with values in linear combinations of graphs. The main property of this invariant is that under certain conditions on the representative of the free graph-link, we can recover this representative from the value invariant on it. In addition, this invariant allows one to partially classify free graph-links.

中文翻译：

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图中值的图链接不变量和图链接的几乎分类

在 [VO Manturov，自由结的几乎分类，Dokl。数学。88(2) (2013) 556–558.] 第二作者构造了一个不变量，它在某种意义上将 Kuperberg 的量子 [公式：见文本] 链接不变量推广到自由链接的情况。在本文中，我们将这种结构推广到自由图链接。结果，我们获得了自由图链接的不变量，其值在图的线性组合中。这个不变量的主要性质是，在一定条件下，自由图链接的代表上，我们可以从它上面的值不变量中恢复这个代表。此外，这个不变量允许人们对自由图链接进行部分分类。