On the Coefficients of Jones Polynomial and Vassiliev Invariants
نویسندگان
چکیده
منابع مشابه
Approximating Jones Coefficients and Other Link Invariants by Vassiliev Invariants
We find approximations by Vassiliev invariants for the coefficients of the Jones polynomial and all specializations of the HOMFLY and Kauffman polynomials. Consequently, we obtain approximations of some other link invariants arising from the homology of branched covers of links.
متن کاملOn Jones knot Invariants and Vassiliev Invariants
We show that the n-th derivative of a quantum group invariant, evaluated at 1, is a Vassiliev invariant while the derivative of the Jones polynomial, evaluated at a real number 6 = 1, is not a Vassiliev in variant. The coeecients of the classical Conway polynomial are known to be Vassiliev invariants. We show that the coeecients of the Jones polynomial are not vassiliev invariants.
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The theory of knot invariants of finite type (Vassiliev invariants) is described. These invariants turn out to be at least as powerful as the Jones polynomial and its numerous generalizations coming from various quantum groups, and it is conjectured that these invariants are precisely as powerful as those polynomials. As invariants of finite type are much easier to define and manipulate than th...
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We study the structure of the stable coefficients of the Jones polynomial of an alternating link. We start by identifying the first four stable coefficients with polynomial invariants of a (reduced) Tait graph of the link projection. This leads us to introduce a free polynomial algebra of invariants of graphs whose elements give invariants of alternating links which strictly refine the first fo...
متن کاملCabling the Vassiliev Invariants
We characterise the cabling operations on the weight systems of finite type knot invariants. The eigenvectors and eigenvalues of this family of operations are described. The canonical deframing projection for these knot invariants is described over the cable eigenbasis. The action of immanent weight systems on general Feynman diagrams is considered, and the highest eigenvalue cabling eigenvecto...
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ژورنال
عنوان ژورنال: Journal of Mathematics Research
سال: 2012
ISSN: 1916-9809,1916-9795
DOI: 10.5539/jmr.v4n6p97