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Contemporary Mathematics. Fundamental Directions, 2013, Volume 51, Pages 33–63 (Mi cmfd253)  
This article is cited in 2 scientific papers (total in 2 papers)

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
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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.
English version:
Journal of Mathematical Sciences, 2016, Volume 214, Issue 5, Pages 632–664
DOI: https://doi.org/10.1007/s10958-016-2803-4
Document Type: Article
UDC: 515.16+519.17
Language: Russian
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 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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