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Mat. Zametki, 2011, Volume 90, Issue 2, Pages 242–253 (Mi mz8740)  

This article is cited in 1 scientific paper (total in 1 paper)

An Invariant of Links in the Thickened Torus

M. V. Zenkina

Moscow State Pedagogical University

Abstract: An invariant of links with two and more components in the thickened torus is constructed; the invariant depends on several variables. The construction uses Kauffman's formal theory, which is based on Dehn's representation of knot groups. This invariant is a natural generalization of a polynomial $z$ constructed by Zenkina and Manturov.

Keywords: link in the thickened torus, virtual knot, invariant of links, link diagram, regular link diagram, shadow of a link diagram, Kaufmann's formal theory, Dehn's presentation

DOI: https://doi.org/10.4213/mzm8740

Full text: PDF file (549 kB)
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English version:
Mathematical Notes, 2011, 90:2, 227–237

Bibliographic databases:

UDC: 515.162.8
Received: 30.03.2010
Revised: 09.10.2010

Citation: M. V. Zenkina, “An Invariant of Links in the Thickened Torus”, Mat. Zametki, 90:2 (2011), 242–253; Math. Notes, 90:2 (2011), 227–237

Citation in format AMSBIB
\Bibitem{Zen11}
\by M.~V.~Zenkina
\paper An Invariant of Links in the Thickened Torus
\jour Mat. Zametki
\yr 2011
\vol 90
\issue 2
\pages 242--253
\mathnet{http://mi.mathnet.ru/mz8740}
\crossref{https://doi.org/10.4213/mzm8740}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2918440}
\transl
\jour Math. Notes
\yr 2011
\vol 90
\issue 2
\pages 227--237
\crossref{https://doi.org/10.1134/S0001434611070224}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000294363500022}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80052040826}


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  • https://doi.org/10.4213/mzm8740
  • http://mi.mathnet.ru/eng/mz/v90/i2/p242

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. V. Zenkina, “An invariant of knots in thickened surfaces”, Journal of Mathematical Sciences, 214:5 (2016), 728–740  mathnet  crossref
  • Математические заметки Mathematical Notes
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