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Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)

 
 

 

On polynomial invariants of virtual links


Author: V. O. Manturov
Translated by: H. H. McFaden
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 65 (2004).
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
Published electronically: October 1, 2004
MathSciNet review: 2193439
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Abstract: The $VA$-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  $VA$-polynomial is proposed. Some properties of the $VA$-polynomial are established. Furthermore, new invariants of virtual links and long virtual knots are constructed.


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Additional Information

V. O. Manturov
Affiliation: Moscow State University, Mechanics and Mathematics Department, 119899 Moscow, Russia
Email: vassily@manturov.mccme.ru

DOI: https://doi.org/10.1090/S0077-1554-04-00140-2
Published electronically: October 1, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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