Research ArticleNo Access

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

Denis P. Ilyutko

http://orcid.org/0000-0003-3184-0494

Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia

E-mail Address: ilyutko@yandex.ru

Corresponding author.

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and

Vassily O. Manturov

Department of Fundamental Sciences, Bauman Moscow State Technical University, Moscow, Russia

E-mail Address: vomanturov@yandex.ru

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https://doi.org/10.1142/S0218216520500637Cited by:0 (Source: Crossref)

Abstract

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 $sl (3)$ $sl (3)$ 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.

Keywords:

AMSC: 16T05, 57M15, 57M25, 57M27

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