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VIRTUAL LINKS WITH NORMAL DIAGRAMS

  • Im, Young-Ho (DEPARTMENT OF MATHEMATICS PUSAN NATIONAL UNIVERSITY)
  • Received : 2009.03.25
  • Accepted : 2009.10.07
  • Published : 2009.12.31

Abstract

We show that if two virtual link diagrams which are normal are equivalent under generalized Reidemeister moves, then they are equivalent under generalized Reidemeister moves preserving the normality of diagrams.

Keywords

References

  1. M. Goussarov, M. Pollyak and O. Viro, Finite type invariants of classical and virtual knots, Topology 39 (2000), 1045-1068. https://doi.org/10.1016/S0040-9383(99)00054-3
  2. N. Kamada, On the Jones polynomials of checkerboard colorable virtual links, Osaka J. Math. 39 (2002), 325-333.
  3. N. Kamada, Some relations on Miyazawa's virtual knot invariant, Topology Appl. 154 (2007), 1417-1429. https://doi.org/10.1016/j.topol.2006.04.025
  4. N. Kamada and S. Kamada, Abstract link diagrams and virtual knots, J. Knot Theory Ramifications 9 (2000), 93-106. https://doi.org/10.1142/S0218216500000049
  5. N. Kamada and S. Nakabo and S. Satoh, A virtualized skein relation for Jones polynomials, Illinois J. Math. 46 (2002), 467-475.
  6. N. Kamada and Y. Miyazawa, A 2-variable polynomial invariant for a virtual link derived from magnetic graphs, Hiroshima Math. J. 35 (2005), 309-326.
  7. L. H. Kauffman, Knots and Phisics, World Scientific, 1992.
  8. L. H. Kauffman, Virtual knot thoery, European J. Combin. 20 (1999), 663-690. https://doi.org/10.1006/eujc.1999.0314