Geodesic
An Invariant of Links in the Thickened Torus
Matematičeskie zametki, Tome 90 (2011) no. 2, pp. 242-253.

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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. 
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M. V. Zenkina. An Invariant of Links in the Thickened Torus. Matematičeskie zametki, Tome 90 (2011) no. 2, pp. 242-253. http://geodesic.mathdoc.fr/item/MZM_2011_90_2_a6/

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