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 CMFD, 2013, Volume 51, Pages 33–63 (Mi cmfd253)

Graph-links: nonrealizability, orientation, and Jones polynomial

D. P. Ilyutkoab, V. S. Safinaa

a Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, Moscow, Russia
b Delone Laboratory of Discrete and Computational Geometry, P. G. Demidov Yaroslavl State University, Yaroslavl, Russia

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.

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English version:
Journal of Mathematical Sciences, 2016, 214:5, 632–664

UDC: 515.16+519.17

Citation: D. P. Ilyutko, V. S. Safina, “Graph-links: nonrealizability, orientation, and Jones polynomial”, Topology, CMFD, 51, PFUR, M., 2013, 33–63; Journal of Mathematical Sciences, 214:5 (2016), 632–664

Citation in format AMSBIB
\Bibitem{IlySaf13} \by D.~P.~Ilyutko, V.~S.~Safina \paper Graph-links: nonrealizability, orientation, and Jones polynomial \inbook Topology \serial CMFD \yr 2013 \vol 51 \pages 33--63 \publ PFUR \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd253} \transl \jour Journal of Mathematical Sciences \yr 2016 \vol 214 \issue 5 \pages 632--664 \crossref{https://doi.org/10.1007/s10958-016-2803-4} 

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This publication is cited in the following articles:
1. D. P. Il'yutko, I. M. Nikonov, “Diagram approach in the theory of knots and its application in the graph theory”, Moscow University Mathematics Bulletin, 73:3 (2018), 124–130
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