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Invariants of virtual rational moves

Noureen A. Khan

Department of Mathematics and Information Sciences, University of North Texas at Dallas, USA

https://doi.org/10.1142/S0218216514500308Cited by:1 (Source: Crossref)

Abstract

Generalized Reidemeister moves provide an extended set of moves to work with virtual knots and links. We introduce virtual tangle moves, generalization of classical rational tangle moves and show that such generalizations are essential to develop new invariants of virtual knots and links. We show that every 2-algebraic virtual link is a virtual 4-move equivalent to a trivial link or Hopf link. The properties of virtual tangle move are analyzed on few existing invariants associated with virtual knots and links.

Keywords:

AMSC: 57M99, 55N20D

References

J. H. Conway, Computational Problems in Abstract Algebra (Pergamon Press, 1969) pp. 329–358. Google Scholar
M. K. Dabkowski , M. Ishiwata and J. H. Przytycki , J. Knot Theory Ramifications 19 , 783 ( 2010 ) . Link, Web of Science, Google Scholar
M. K. Dabkowski et al. , J. Knot Theory Ramifications 20 , 47 ( 2011 ) . Link, Web of Science, Google Scholar
S. Jablan, L. Radovic, R. Sazdanovic and A. Zekovic, Virtual knots and links, http://math.ict.edu.rs:8080/webMathematica . Google Scholar
L. H. Kauffman, European J. Combin. 20(7), 662 (1999). Crossref, Web of Science, Google Scholar
V. O. Mantrurov and D. P. Ilyutko , Virtual Knots: The State of the Art , Series on Knots and Everything 51 ( World Scientific Press , 2012 ) . Link, Google Scholar