Polynomial invariants and Vassiliev invariants

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dc.creatorJeong, Myeong-Ju
dc.creatorPark, Chan-Young
dc.date2002-11-04
dc.date.accessioned2026-07-07T04:52:37Z
dc.date.available2026-07-07T04:52:37Z
dc.descriptionWe give a criterion to detect whether the derivatives of the HOMFLY polynomial at a point is a Vassiliev invariant or not. In particular, for a complex number b we show that the derivative P_K^{(m,n)}(b,0)=d^m/da^m d^n/dx^n P_K(a,x)|(a, x) = (b, 0) of the HOMFLY polynomial of a knot K at (b,0) is a Vassiliev invariant if and only if b= -+1. Also we analyze the space V_n of Vassiliev invariants of degree <=n for n = 1,2,3,4,5 by using the bar-operation and the star-operation in [M-J Jeong, C-Y Park, Vassiliev invariants and knot polynomials, to appear in Topology and Its Applications]. These two operations are unified to the hat-operation. For each Vassiliev invariant v of degree <=n, hat(v) is a Vassiliev invariant of degree <=n and the value hat(v)K) of a knot K is a polynomial with multi-variables of degree <=n and we give some questions on polynomial invariants and the Vassiliev invariants.
dc.descriptionPublished by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper7.abs.html
dc.identifierhttps://arxiv.org/abs/math/0211045
dc.identifierhttp://arxiv.org/abs/math/0211045
dc.identifierGeom. Topol. Monogr. 4 (2002) 89-101
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65529
dc.subjectGeometric Topology
dc.subject57M25
dc.titlePolynomial invariants and Vassiliev invariants
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