Cabling procedure for the colored HOMFLY polynomials
نویسندگان
چکیده
منابع مشابه
THE COLORED HOMFLY POLYNOMIAL IS q-HOLONOMIC
We prove that the colored HOMFLY polynomial of a link, colored by symmetric or exterior powers of the fundamental representation, is q-holonomic with respect to the color parameters. As a result, we obtain the existence of an (a, q) super-polynomial of all knots in 3-space. Our result has implications on the quantization of the SL(2,C) character variety of knots using ideal triangulations or th...
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We calculate the dimensions of the space of Vassiliev invariants coming from the Homfly polynomial of links, and of the space of Vassiliev invariants coming from the Kauffman polynomial of links. We show that the intersection of these spaces is spanned by the Vassiliev invariants coming from the Jones polynomial and from a polynomial called Υ. We also show that linearly independent Vassiliev in...
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We study the behavior of the degree of the colored Jones polynomial and the boundary slopes of knots under the operation of cabling. We show that, under certain hypothesis on this degree, if a knot K satisfies the Slope Conjecture then a (p, q)-cable of K satisfies the conjecture, provided that p/q is not a Jones slope of K. As an application we prove the Slope Conjecture for iterated cables of...
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A celebrated result of F. Jaeger states that the Tutte polynomial of a planar graph is determined by the HOMFLY polynomial of an associated link. Here we are interested in the converse of this result. We consider the question ‘to what extent does the Tutte polynomial determine the HOMFLY polynomial of any knot?’ We show that the HOMFLY polynomial of a knot is determined by Tutte polynomials of ...
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ژورنال
عنوان ژورنال: Theoretical and Mathematical Physics
سال: 2014
ISSN: 0040-5779,1573-9333
DOI: 10.1007/s11232-014-0129-2