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A NOTE ON NON-CLASSICAL VIRTUAL KNOTS

TOSHIMASA KISHINO

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

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and

SHIN SATOH

Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa-Oiwake, Kyoto, 606-8502, Japan

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https://doi.org/10.1142/S0218216504003548Cited by:39 (Source: Crossref)

Abstract

The first aim of this paper is to give an example of a virtual knot which vanishes all the known invariants and to show that it is a non-classical (in particular, non-trivial) knot. The second is to study some properties of the Z-polynomial of a virtual knot with virtual crossing number one and to show that there are infinitely many virtual knots with virtual crossing number two.

Keywords:

AMSC: Primary 57M25, Secondary 57M27

References

D. Hrencecin and L. H. Kauffman, On filamentations and virtual knots, preprint, http://xxx.lanl.gov/abs/math.GT/0112206 . Google Scholar
L. H. Kauffman, European J. Combin. 20, 663 (1999). Crossref, Web of Science, Google Scholar
L. H. Kauffman and D. E. Radford, Bi-oriented quantum algebras, and a generalized Alexander polynomial for virtual links, preprint, http://xxx.lanl.gov/abs/math.GT/0112280 . Google Scholar
M. Goussarov, M. Polyak and O. Viro, Topology 39, 1045 (2000). Crossref, Web of Science, Google Scholar
F. Jaeger, L. J. Kauffman and H. Saleur, J. Combin. Theory Ser. B61, 237 (1994). Google Scholar
J. Sawollek, On Alexander–Conway polynomials for virtual knots and links, preprint, http://xxx.lanl.gov/abs/math.GT/9912173 . Google Scholar
D. S. Silver and S. G. Williams, Alexander groups and virtual links, to appear in J. Knot Theory Ramifications . Google Scholar