Polynomial perception of exponential growth: A reply to Jones
نویسندگان
چکیده
منابع مشابه
Colored Jones Polynomials with Polynomial Growth
Abstract. The volume conjecture and its generalizations say that the colored Jones polynomial corresponding to the N-dimensional irreducible representation of sl(2;C) of a (hyperbolic) knot evaluated at exp(c/N) grows exponentially with respect to N if one fixes a complex number c near 2π √ −1. On the other hand if the absolute value of c is small enough, it converges to the inverse of the Alex...
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توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولIs the Jones Polynomial of a Knot Really a Polynomial?
The Jones polynomial of a knot in 3-space is a Laurent polynomial in q, with integer coefficients. Many people have pondered why is this so, and what is a proper generalization of the Jones polynomial for knots in other closed 3-manifolds. Our paper centers around this question. After reviewing several existing definitions of the Jones polynomial, we show that the Jones polynomial is really an ...
متن کاملAsymptotics 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: Perception & Psychophysics
سال: 1977
ISSN: 0031-5117,1532-5962
DOI: 10.3758/bf03198727