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Vassiliev invariants of type two for a link
Author(s):
Hitoshi
Murakami
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3889-3896.
MSC (1991):
Primary 57M25
MathSciNet review:
1353392
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Abstract:
We show that any type two Vassiliev invariant of a link can be expressed as a linear combination of the second coefficients of the Conway polynomials of its components and a quadratic expression of linking numbers.
References:
- 1.
- D. Bar-Natan, On the Vassiliev knot invariant, Topology 34 (1995), 423-472. CMP 95:08
- 2.
- J.S. Birman, New points of view in knot theory, Bull. Amer. Math. Soc. (N.S.) 28 (1993), 253-287. MR 94b:57007
- 3.
- J.S. Birman and X.-S. Lin, Knot polynomials and Vassiliev's invariants, Invent. Math. 111 (1993), 225-270. MR 94d:57010
- 4.
- T. Kanenobu and Y. Miyazawa, Link polynomials as Vassiliev-type invariants, preprint, Osaka City Univ. and Yamaguchi Univ., 1994.
- 5.
- Y. Miyazawa, Vassiliev's invariant and link polynomials (in Japanese), Teijigen-Tayotai no Toporojii to Musubime-riron (Topology of Low-dimensional Manifolds and Knot Theory), Proceedings of Research Institute for Mathematics and Computer Science, vol. 9, Tsuda College, 1994.
- 6.
- H. Murakami, On derivatives of the Jones polynomial, Kobe J. Math. 3 (1986), 61-64. MR 88a:57015
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- A. Tani, Vassiliev type invariant of order
 (in Japanese), Teijigen-Tayotai no Toporojii to Musubime-riron (Topology of Low-dimensional Manifolds and Knot Theory), Proceedings of Research Institute for Mathematics and Computer Science, vol. 9, Tsuda College, 1994. - 9.
- V.A. Vassiliev, Cohomology of knot spaces, Theory of Singularities and Its Applications (V.I. Arnold, ed.), Advances in Soviet Math., vol. 1, Amer. Math. Soc., 1990. MR 92a:57016
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Additional Information:
Hitoshi
Murakami
Affiliation:
Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558, Japan
Address at time of publication:
Department of Mathematics, School of Science and Engineering, Waseda University, Ohkubo, Tokyo, 169, Japan
Email:
hitoshi@haya.co.jp
DOI:
10.1090/S0002-9939-96-03628-3
PII:
S 0002-9939(96)03628-3
Keywords:
Vassiliev invariant,
Conway polynomial
Received by editor(s):
March 15, 1995
Additional Notes:
Partially supported by Grant-in-Aid for Scientific Research on Priority Area 231 ``Infinite Analysis'', the Ministry of Education, Science and Culture, Japan.
Communicated by:
Ronald Stern
Copyright of article:
Copyright
1996,
American Mathematical Society
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