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Zap. Nauchn. Sem. POMI, 2009, Volume 372, Pages 5–18 (Mi znsl3553)  

This article is cited in 3 scientific papers (total in 3 papers)

An invariant of links in a thickened torus

M. V. Zenkina, V. O. Manturov

Moscow State Region University, Faculty of Physics and Mathematics, Moscow, Russia

Abstract: For links in a thickened torus, we construct a polynomial invariant depending on three variables. The construction involves Kauffman's formal theory based on Dehn's presentation of the group of a knot. Certain properties of the invariant are established, and a theorem about a Conway type relation is proved. Bibl. – 10 titles.

Key words and phrases: Alexander polynomial, Conway type relations, textil structres.

Full text: PDF file (279 kB)
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English version:
Journal of Mathematical Sciences (New York), 2011, 175:5, 501–508

UDC: 515.162.8
Received: 07.11.2009

Citation: M. V. Zenkina, V. O. Manturov, “An invariant of links in a thickened torus”, Geometry and topology. Part 11, Zap. Nauchn. Sem. POMI, 372, POMI, St. Petersburg, 2009, 5–18; J. Math. Sci. (N. Y.), 175:5 (2011), 501–508

Citation in format AMSBIB
\Bibitem{ZenMan09}
\by M.~V.~Zenkina, V.~O.~Manturov
\paper An invariant of links in a~thickened torus
\inbook Geometry and topology. Part~11
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 372
\pages 5--18
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3553}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 175
\issue 5
\pages 501--508
\crossref{https://doi.org/10.1007/s10958-011-0359-x}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79958030657}


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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 Links in the Thickened Torus”, Math. Notes, 90:2 (2011), 227–237  mathnet  crossref  crossref  mathscinet  isi
    2. D. P. Ilyutko, V. O. Manturov, I. M. Nikonov, “Parity in knot theory and graph-links”, Journal of Mathematical Sciences, 193:6 (2013), 809–965  mathnet  crossref  mathscinet
    3. M. V. Zenkina, “An invariant of knots in thickened surfaces”, Journal of Mathematical Sciences, 214:5 (2016), 728–740  mathnet  crossref
  • Записки научных семинаров ПОМИ
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