We prove that the number of linearly independent Vassiliev invariants for an r-component link of order n, which derived from the HOMFLY polynomial, is greater than or equal to min{n,[(n+r-1)/2]}.
@article{bwmeta1.element.bwnjournal-article-bcpv42i1p165bwm,
author = {Kanenobu, Taizo and Miyazawa, Yasuyuki},
title = {Homfly polynomials as vassiliev link invariants},
journal = {Banach Center Publications},
volume = {43},
year = {1998},
pages = {165-185},
zbl = {0901.57017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p165bwm}
}
Kanenobu, Taizo; Miyazawa, Yasuyuki. Homfly polynomials as vassiliev link invariants. Banach Center Publications, Tome 43 (1998) pp. 165-185. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p165bwm/
[000] [BN] D. Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995), 423-472. | Zbl 0898.57001
[001] [B1] J. S. Birman, New points of view in knot theory, Bull. Amer. Math. Soc. 28 (1993), 253-287. | Zbl 0785.57001
[002] [B2] J. S. Birman, On the combinatorics of Vassiliev invariants, Braid group, knot theory and statistical mechanics II (M. L. Ge and C. N. Yang, eds.), Advanced Series in Mathematical Physics, World Scientific, Singapore-New Jersey-London-Hong Kong 1994, pp. 1-19.
[003] [BL] J. S. Birman and X.-S. Lin, Knot polynomials and Vassiliev's invariants, Invent. Math. 111 (1993), 225-270. | Zbl 0812.57011
[004] [CD] S. V. Chmutov and S. V. Duzhin, An upper bound for the number of Vassiliev knot invariants, J. Knot Theory Ramifications 3 (1994), 141-151. | Zbl 0816.57005
[005] [C] J. H. Conway, An enumeration of knots and links, Computational Problems in Abstract Algebra (J. Leech, ed.), Pergamon Press, New York, 1969, pp. 329-358.
[006] [FYHLMO] P. Freyd, D. Yetter, J. Hoste, W. B. R. Lickorish, K. Millett and A. Ocneanu, A new polynomial invariant of knots and links, Bull. Amer. Math. Soc. 12 (1985), 239-246. | Zbl 0572.57002
[007] [G] M. N. Gusarov, A new form of the Conway-Jones polynomial of oriented links, Zap. Nauchn. Sem. Len. Otdel Mat. Inst. Steklov (LOMI) 193 (1991), Geom. i Topol. 1, 4-9; English translation: Topology of manifolds and varieties, Advances in Soviet Mathematics. Vol. 18, Amer. Math. Soc., Providence, RI, 1994, pp. 167-172.
[008] [H] J. Hoste, The first coefficient of the Conway polynomial, Proc. Amer. Math. Soc. 95 (1985), 299-302. | Zbl 0576.57005
[009] [J] V. F. R. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. Math. 126 (1987), 335-388. | Zbl 0631.57005
[010] [Kf] L. H. Kauffman On Knots, Ann. of Math. Studies 115, Princeton Univ. Press, Princeton, 1987.
[011] [Kw] A. Kawauchi On coefficient polynomials of the skein polynomial of an oriented link, Kobe J. Math. 11 (1994), 49-68. | Zbl 0861.57013
[012] [L] J. Lannes Sur les invariants de Vassiliev de degré inférieur ou égal à 3, Enseign. Math. (2) 39 (1993), 295-316.
[013] [LM] W. B. R. Lickorish and K. C. Millett, A polynomial invariant of oriented links, Topology 26 (1987), 107-141. | Zbl 0608.57009
[014] [MM] P. Melvin and H. R. Morton, The coloured Jones function, Commun. Math. Phys. 169 (1995), 501-520. | Zbl 0845.57007
[015] [Me] G. Meng, Bracket models for weight systems and the universal Vassiliev invariants, Topology Appl. 76 (1997), 47-60. | Zbl 1001.57028
[016] [Mi] Y. Miyazawa, The third derivative of the Jones polynomial, J. Knot Theory Ramifications, (to appear). | Zbl 0885.57004
[017] [Mu1] H. Murakami, On derivatives of the Jones polynomial, Kobe J. Math. 3 (1986), 61-64. | Zbl 0624.57003
[018] [Mu2] H. Murakami, Vassiliev type invariant of order two for a link, Proc. Amer. Math. Soc. 124 (1996), 3889-3896. | Zbl 0874.57004
[019] [N] K. Y. Ng, Groups of ribbon knots, preprint.
[020] [PT] J. H. Przytycki and P. Traczyk, Invariants of links of Conway type, Kobe J. Math. 4 (1987), 115-139. | Zbl 0655.57002
[021] [R] D. Rolfsen Knots and Links, Lecture Series no. 7, Publish or Perish, Berkeley, 1976.
[022] [S1] T. Stanford, Finite-type invariants of knots, links, and graphs, Topology 35 (1996), 1027-1050. | Zbl 0863.57005
[023] [S2] T. Stanford, The functoriality of Vassiliev-type invariants of links, braids, and knotted graphs, J. Knot Theory Ramifications 3 (1994) 247-262. | Zbl 0841.57018
[024] [V] V. A. Vassiliev, Cohomology of knot spaces, Theory of Singularities and its Applications (V. I. Arnold, ed.), Advances in Soviet Mathematics, Vol. 1, Amer. Math. Soc., Providence, RI, 1990, pp. 23-69.