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CMFD, 2013, Volume 51, Pages 21–32 (Mi cmfd252)  

An invariant of knots in thickened surfaces

M. V. Zenkina

Faculty of Mathematics, Moscow State Pedagogical University, Moscow, Russia

Abstract: In the present paper, we construct an invariant of knots in the thickened sphere with $g$g handles dependent on $2g+3$ variables. In the construction of the invariant we use the Wirtinger presentation of the knot group and the concept of parity introduced by Manturov [9]. In the present paper, we also consider examples of knots in the thickened torus considered in [2] such that their nonequivalence is proved by using the constructed polynomial.

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English version:
Journal of Mathematical Sciences, 2016, 214:5, 728–740

UDC: 515.162.8

Citation: M. V. Zenkina, “An invariant of knots in thickened surfaces”, Topology, CMFD, 51, PFUR, M., 2013, 21–32; Journal of Mathematical Sciences, 214:5 (2016), 728–740

Citation in format AMSBIB
\Bibitem{Zen13}
\by M.~V.~Zenkina
\paper An invariant of knots in thickened surfaces
\inbook Topology
\serial CMFD
\yr 2013
\vol 51
\pages 21--32
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd252}
\transl
\jour Journal of Mathematical Sciences
\yr 2016
\vol 214
\issue 5
\pages 728--740
\crossref{https://doi.org/10.1007/s10958-016-2809-y}


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