Graph-Links: Nonrealizability, Orientation, and Jones Polynomial
- Authors: Ilyutko D.P.1, Safina V.S.1
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Affiliations:
- M. V. Lomonosov Moscow State University
- Issue: Vol 214, No 5 (2016)
- Pages: 632-664
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237482
- DOI: https://doi.org/10.1007/s10958-016-2803-4
- ID: 237482
Cite item
Abstract
The present paper is devoted to graph-links with many components and consists of two parts. In the first part of the paper we classify vertices of a labeled graph according to the component they belong to. Using this classification, we construct an invariant of graph-links. This invariant shows that the labeled second Bouchet graph generates a nonrealizable graph-link.
In the second part of the work we introduce the notion of an oriented graph-link. We define a writhe number for the oriented graph-link and we get an invariant of oriented graph-links, the Jones polynomial, by normalizing the Kauffman bracket with the writhe number.
About the authors
D. P. Ilyutko
M. V. Lomonosov Moscow State University
Author for correspondence.
Email: ilyutko@yandex.ru
Russian Federation, Moscow
V. S. Safina
M. V. Lomonosov Moscow State University
Email: ilyutko@yandex.ru
Russian Federation, Moscow