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Detecting Non-Triviality of Virtual Links

Teruhisa Kadokami

Department of Mathematics, Osaka City University, Sugimoto 3-3-138, Sumiyoshi-ku, Osaka 558-8585, Japan

https://doi.org/10.1142/S0218216503002780Cited by:26 (Source: Crossref)

Abstract

J. S. Carter, S. Kamada and M. Saito showed that there is one to one correspondence between the virtual Reidemeister equivalence classes of virtual link diagrams and the stable equivalence classes of link diagrams on compact oriented surfaces. Using the result, we show how to obtain the supporting genus of a projected virtual link by a geometric method. From this result, we show that a certain virtual knot which cannot be judged to be non-trivial by known algebraic invariants is non-trivial, and we suggest to classify the equivalence classes of projected virtual links by using the supporting genus.

Keywords:

References

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