Kyungpook Mathematical Journal

  • 제49권4호
  • /
  • Pages.801-809
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  • 2009
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Knots with a Trivial Coefficient Polynomial

  • 투고 : 2009.04.05
  • 심사 : 2009.07.21
  • 발행 : 2009.12.31
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초록

By using a tangle decomposition of a knot, we give a method for the construction of a knot with the lowest trivial HOMFLY coefficient polynomial. Applying this, we show that there exist infinitely many 2-bridge knots with such a coefficient polynomial.

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참고문헌

  1. J. H. Conway, An enumeration of knots and links, in "Computational Problems in Abstract Algebra", (J. Leech, ed.), Pergamon Press, New York, 1969, pp. 329-358.
  2. P. Freyd, D. Yetter, J. Hoste, W. B. R. Lickorish, K. C. Millett and A. Ocneanu, A new polynomial invariant of knots and links, Bull. Amer. Math. Soc., 12(1985), 239-246. https://doi.org/10.1090/S0273-0979-1985-15361-3
  3. Y. Fujino, Y. Miyazawa and K. Nakajima, H(n)-unknotting number of a knot, in Proceedings of the Conference "Knots and Low Dimensional Manifolds", (1997), 72-85.
  4. J. Hoste, Y. Nakanishi and K. Taniyama, Unknotting operations involving trivial tangles, Osaka J. Math., 27(1990), 555-566.
  5. T. Kanenobu, Kauffman polynomials as Vassiliev link invariants, in "Knots 96", (S. Suzuki, ed.), World Scientific, 1997, pp. 411-431.
  6. L. H. Kauffman, An invariant of regular isotopy, Trans. Amer. Math. Soc., 318(1990), 417-471. https://doi.org/10.2307/2001315
  7. A. Kawauchi, Almost identical link imitations and the skein polynomial, in "Knots 90", (A. Kawauchi, ed.), Walter de Gruyter, Berlin-New York, 1992, pp. 465-476.
  8. W. B. R. Lickorish, An Introduction to Knot Theory, Graduate Texts in Mathematics, 175 Springer-Verlag, 1986.
  9. W. B. R. Lickorish and K. C. Millett, A polynomial invariant of oriented links, Topology, 26(1987), 107-141.
  10. J. H. Przytycki and P. Traczyk, Invariants of links of Conway type, Kobe J. Math., 4(1987), 115-139.

피인용 문헌

  1. On Seifert Matrices of Symmetric Links vol.51, pp.3, 2011, https://doi.org/10.5666/KMJ.2011.51.3.261