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Moscow Mathematical Journal, 2007, Volume 7, Number 3, Pages 409–418
DOI: https://doi.org/10.17323/1609-4514-2007-7-3-409-418 (Mi mmj288) 		 
This article is cited in 41 scientific papers (total in 41 papers)

The Kauffman bracket of virtual links and the Bollobás–Riordan polynomial

S. V. Chmutova, I. M. Pakb

a Ohio State University
b Massachusetts Institute of Technology
Full-text PDF Citations (41)
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DOI: https://doi.org/10.17323/1609-4514-2007-7-3-409-418
Abstract: We show that the Kauffman bracket $[L]$ of a checkerboard colorable virtual link $L$ is an evaluation of the Bollobás–Riordan polynomial $R_{G_L}$ of a ribbon graph associated with $L$. This result generalizes the celebrated relation between the classical Kauffman bracket and the Tutte polynomial of planar graphs.
Key words and phrases: Virtual knots and links, knot invariants, Jones polynomial, Kauffman bracket, Tutte polynomial, Bollobás–Riordan polynomial, ribbon graph.
Received: June 20, 2006
Bibliographic databases:
MSC: 57M15, 57M27, 05C10, 05C22
Language: English
Citation: S. V. Chmutov, I. M. Pak, “The Kauffman bracket of virtual links and the Bollobás–Riordan polynomial”, Mosc. Math. J., 7:3 (2007), 409–418
Citation in format AMSBIB
\Bibitem{ChmPak07}
\by S.~V.~Chmutov, I.~M.~Pak
\paper The Kauffman bracket of virtual links and the Bollob\'as--Riordan polynomial
\jour Mosc. Math.~J.
\yr 2007
\vol 7
\issue 3
\pages 409--418
\mathnet{http://mi.mathnet.ru/mmj288}
\crossref{https://doi.org/10.17323/1609-4514-2007-7-3-409-418}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2343139}
\zmath{https://zbmath.org/?q=an:1155.57004}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000261829400003}
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