Abstract
In [1], we have constructed a polynomial invariant of regular isotopy, , for oriented knot and link diagrams L. From by multiplying it by normalizing factor, we obtained an ambient isotopy invariant, , for oriented knotsand links. In this paper, we give some properties of these polynomials. Wealso calculate the polynomials and of the knots through nine crossings and thetwo-component links through eight crossing
Keywords
G-polynomial N-polinomial Jones Polynomial regular isotopy ambient isotopy tables of knots and links
References
- Altintas, I., An oriented state model for the Jones polynomial and its applications alternating links, Applied Mathematics and Computation, 194, (2007), 168-178.
- Jones, V.F.R., A new knot polynomial and Von Neuman algebras, Notices. Amer. Math. Soc., (1985).
- Jones, V.F.R., A new knot polynomial and Von Neuman algebras, Bul. Amer. Math. Soc. 12, (1985), 103-111.
- Jones, V.F.R., Hecke algebra representations of braid groups and link polynomial, Ann. Math., 126, (1987), 335-388.
- Kauffman, L.H., State models and the Jones polynomial, Topology, 26, (1987), 395-407.
- Kauffman, L.H., New invariants in the theory of knots, Amer. Math. Monthly vol. 95, (1988), 195-2
- Kauffman, L.H., An invariant of regular isotopy, Trans. Amer. Math. Soc. 318, (1990), 417- 4
- Kauffman, L.H., Knot and physics, Worıd ScientiŞc, (1991), (second edition 1993).
- Tait, P. G., On Knots I,II,III., ScientiŞc Papers Vol. I, Cambridge University Press, London, (1898), 273-347.
- Kirkman, T.P., The enumeration, description and construction of knots with fewer than 10 crossings, Trans.R.Soc. Edinb., 32, (1865), 281-309.[9]
- Little, C.N., Non-alternate µ− knots, Trans.R.Soc. Edinb., 35, (1889), 663-664.
- Murasugi, K., Knot theory and its applications, translated by Kurpito, B., Birkhause, Boston, (1996).
- Rolfsen, D., Knot and Links, Mathematics Lectures Series No. 7 Publish or Perish Press, (1976).
- Kauffman, L.H., On knots, Princeton University Pres, Princeton, New Jersey, (1987). www.knotplot.com
Abstract
References
- Altintas, I., An oriented state model for the Jones polynomial and its applications alternating links, Applied Mathematics and Computation, 194, (2007), 168-178.
- Jones, V.F.R., A new knot polynomial and Von Neuman algebras, Notices. Amer. Math. Soc., (1985).
- Jones, V.F.R., A new knot polynomial and Von Neuman algebras, Bul. Amer. Math. Soc. 12, (1985), 103-111.
- Jones, V.F.R., Hecke algebra representations of braid groups and link polynomial, Ann. Math., 126, (1987), 335-388.
- Kauffman, L.H., State models and the Jones polynomial, Topology, 26, (1987), 395-407.
- Kauffman, L.H., New invariants in the theory of knots, Amer. Math. Monthly vol. 95, (1988), 195-2
- Kauffman, L.H., An invariant of regular isotopy, Trans. Amer. Math. Soc. 318, (1990), 417- 4
- Kauffman, L.H., Knot and physics, Worıd ScientiŞc, (1991), (second edition 1993).
- Tait, P. G., On Knots I,II,III., ScientiŞc Papers Vol. I, Cambridge University Press, London, (1898), 273-347.
- Kirkman, T.P., The enumeration, description and construction of knots with fewer than 10 crossings, Trans.R.Soc. Edinb., 32, (1865), 281-309.[9]
- Little, C.N., Non-alternate µ− knots, Trans.R.Soc. Edinb., 35, (1889), 663-664.
- Murasugi, K., Knot theory and its applications, translated by Kurpito, B., Birkhause, Boston, (1996).
- Rolfsen, D., Knot and Links, Mathematics Lectures Series No. 7 Publish or Perish Press, (1976).
- Kauffman, L.H., On knots, Princeton University Pres, Princeton, New Jersey, (1987). www.knotplot.com
Details
| Primary Language | English |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | December 1, 2013 |
| Submission Date | March 9, 2015 |
| Published in Issue | Year 2013 Volume: 1 Issue: 2 |
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