The Jones Polynomial
نویسنده
چکیده
A link is a finite family of disjoint, smooth, oriented or unoriented, closed curves in R or equivalently S. A knot is a link with one component. The Jones polynomial VL(t) is a Laurent polynomial in the variable √ t which is defined for every oriented link L but depends on that link only up to orientation preserving diffeomorphism, or equivalently isotopy, of R. Links can be represented by diagrams in the plane and the Jones polynomials of the simplest links are given below.
منابع مشابه
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We study relationships between the colored Jones polynomial and the A-polynomial of a knot. We establish for a large class of 2-bridge knots the AJ conjecture (of Garoufalidis) that relates the colored Jones polynomial and the A-polynomial. Along the way we also calculate the Kauffman bracket skein module of all 2-bridge knots. Some properties of the colored Jones polynomial of alternating knot...
متن کاملA volume-ish theorem for the Jones polynomial of alternating knots
The Volume conjecture claims that the hyperbolic Volume of a knot is determined by the colored Jones polynomial. The purpose of this article is to show a Volume-ish theorem for alternating knots in terms of the Jones polynomial, rather than the colored Jones polynomial: The ratio of the Volume and certain sums of coefficients of the Jones polynomial is bounded from above and from below by const...
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We prove a relation in the algebra of the Jones Vassiliev invariants, giving a new restriction to the values of the Jones polynomial on knots, and the non-existence of another family of such relations. We prove, that Jones polynomials of positive knots have non-negative minimal degree and extend this result to k-almost positive knots. We prove that if a positive knot is alternating, then all it...
متن کامل2 00 3 Categorifications of the colored Jones polynomial
The colored Jones polynomial of links has two natural normalizations: one in which the n-colored unknot evaluates to [n + 1], the quantum dimension of the (n + 1)-dimensional irreducible representation of quantum sl(2), and the other in which it evaluates to 1. For each normalization we construct a bigraded cohomology theory of links with the colored Jones polynomial as the Euler characteristic.
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تاریخ انتشار 2005