Tackling Fluid Structures Complexity by the Jones Polynomial
نویسندگان
چکیده
منابع مشابه
The Jones Polynomial
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 dia...
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We study the distribution of zeroes of the Jones polynomial VK (t) for a knot K . We have computed numerically the roots of the Jones polynomial for all prime knots with N 6 10 crossings, and found the zeroes scattered about the unit circle |t|=1 with the average distance to the circle approaching a nonzero value as N increases. For torus knots of the type (m; n) we show that all zeroes lie on ...
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15 صفحه اولAsymptotics of the Colored Jones Polynomial and the A-polynomial
The N-colored Jones polynomial JK (N) is a quantum invariant which is defined based on the N-dimensional irreducible representation of the quantum group Uq(sl(2)). Motivated by Volume Conjecture raised by Kashaev [16], it was pointed out that the colored Jones polynomial at a specific value should be related to the hyperbolic volume of knot complement [21]. As another example of the knot invari...
متن کاملThe Colored Jones Polynomial and the A-polynomial of Knots
We study relationships between the colored Jones polynomial and the A-polynomial of a knot. The AJ conjecture (of Garoufalidis) that relates the colored Jones polynomial and the A-polynomial is established for a large class of two-bridge knots, including all twist knots. We formulate a weaker conjecture and prove that it holds for all two-bridge knots. Along the way we also calculate the Kauffm...
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ژورنال
عنوان ژورنال: Procedia IUTAM
سال: 2013
ISSN: 2210-9838
DOI: 10.1016/j.piutam.2013.03.021