Matrix integral expansion of colored Jones polynomials for figure-eight knot
نویسندگان
چکیده
منابع مشابه
Some Limits of the Colored Jones Polynomials of the Figure-eight Knot
We will study the asymptotic behaviors of the colored Jones poly-nomials of the figure-eight knot. In particular we will show that for certain limits we obtain the volumes of the cone manifolds with singularities along the knot.
متن کاملThe Colored Jones Polynomials and the Alexander Polynomial of the Figure-eight Knot
Abstract. The volume conjecture and its generalization state that the series of certain evaluations of the colored Jones polynomials of a knot would grow exponentially and its growth rate would be related to the volume of a threemanifold obtained by Dehn surgery along the knot. In this paper, we show that for the figure-eight knot the series converges in some cases and the limit equals the inve...
متن کاملThe Colored Jones Polynomials of the Figure-eight Knot and Its Dehn Surgery Spaces
Let K be a knot and JN (K; t) be the colored Jones polynomial of K in the three-sphere S corresponding to the N -dimensional representation of sl2(C) (see for example [4]). We normalize it so that JN (unknot; t) = 1. In [3], R. Kashaev introduced a series of numerical link invariants and proposed a conjecture that a limit of his invariants would determines the hyperbolic volume of the complemen...
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The N-colored Jones polynomial JK (N) is one of the quantum invariants for knot K . It is associated with the N-dimensional irreducible representation of sl(2), and is powerful to classify knots. Motivated by “volume conjecture” [12, 18] saying that a hyperbolic volume of the knot complement dominates an asymptotic behavior of the colored Jones polynomial JK (N) at q = e2πi/N , it receives much...
متن کاملAsymptotic Behaviors of the Colored Jones Polynomials of a Torus Knot
Let K be a knot in the three-sphere and JN (K; t) the colored Jones polynomial corresponding to the N -dimensional representation of sl2(C) normalized so that JN (unknot; t) = 1 [8, 12]. R. Kashaev found a series of link invariants parameterized by positive integers [9] and proposed a conjecture that the asymptotic behavior of his invariants would determine the hyperbolic volume of the knot com...
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ژورنال
عنوان ژورنال: JETP Letters
سال: 2015
ISSN: 0021-3640,1090-6487
DOI: 10.1134/s0021364015010026