Colored Jones polynomials with polynomial growth
Geometric Topology
2008-04-19 v2 Mathematical Physics
math.MP
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 2*Pi*I. On the other hand if the absolute value of c is small enough, it converges to the inverse of the Alexander polynomial evaluated at exp(c). In this paper we study cases where it grows polynomially.
Cite
@article{arxiv.0711.2836,
title = {Colored Jones polynomials with polynomial growth},
author = {Kazuhiro Hikami and Hitoshi Murakami},
journal= {arXiv preprint arXiv:0711.2836},
year = {2008}
}
Comments
17 pages, to appear in Commun. Contemp. Math