Geodesic
An invariant of knots in thickened surfaces
Contemporary Mathematics. Fundamental Directions, Topology, Tome 51 (2013), pp. 21-32.

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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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M. V. Zenkina. An invariant of knots in thickened surfaces. Contemporary Mathematics. Fundamental Directions, Topology, Tome 51 (2013), pp. 21-32. http://geodesic.mathdoc.fr/item/CMFD_2013_51_a1/

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