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Linear independence of derivatives of link polynomials. (English) Zbl 0992.57007
Higher order link polynomials were introduced by the author [J. Lond. Math. Soc., II. Ser. 56, No. 1, 189-208 (1997; Zbl 0903.57002)] and independently by J. E. Andersen and V. Turaev [J. Knot Theory Ramifications 8, No. 8, 963-984 (1999; Zbl 0991.57015)]. In the present paper the partial derivatives of the HOMFLY polynomial are shown to be linearly independent, and certain evaluations of these partial derivatives are shown to generate all higher order Conway polynomials.
MSC:
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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References:
[1] Andersen, J.E.; Turaev, V., Higher skein modules, J. knot theory ramifications, 8, 963-984, (1999) · Zbl 0991.57015
[2] Lickorish, W.B.R.; Rong, Y., On derivatives of link polynomials, Topology appl., 87, 63-71, (1998) · Zbl 0927.57008
[3] Y. Miyazawa, The Kauffman polynomials of order 1, in preparation
[4] Rong, Y., Link polynomials of higher order, J. London math. soc. (2), 56, 189-208, (1997) · Zbl 0903.57002
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