SOME PROPERTIES OF POLYNOMIALS G AND N, AND TABLES OF KNOTS AND LINKS
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
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]