On polynomial invariants of virtual links
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V. O. Manturov
Translated by: H. H. McFaden - Trans. Moscow Math. Soc. 2004, 161-175
- DOI: https://doi.org/10.1090/S0077-1554-04-00140-2
- Published electronically: October 1, 2004
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Abstract:
The $V\!A$-polynomial proposed in the author’s earlier paper (Acta Appl. Math. 72 (2002), 295–309) for virtual knots and links is considered in this paper. One goal here is to refine the definition of this polynomial to the case of the ring ${\mathbb Z}$ in place of the field ${\mathbb Q}$. Moreover, the approach in the paper mentioned makes it possible to recognize “long virtual knots” obtained from equivalent virtual knots by cutting at various points. An invariant of long virtual knots that is based on the same technique as the $V\!A$-polynomial is proposed. Some properties of the $V\!A$-polynomial are established. Furthermore, new invariants of virtual links and long virtual knots are constructed.References
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Bibliographic Information
- V. O. Manturov
- Affiliation: Moscow State University, Mechanics and Mathematics Department, 119899 Moscow, Russia
- Email: vassily@manturov.mccme.ru
- Published electronically: October 1, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2004, 161-175
- MSC (2000): Primary 57M27, 57M25; Secondary 12E10
- DOI: https://doi.org/10.1090/S0077-1554-04-00140-2
- MathSciNet review: 2193439