An invariant of graph-links valued in graphs and an almost classification of graph-links

摘要

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 sl(3) 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.