Kazuhiro Hikami, Hitoshi Murakami
Published 2007-11-19, updated 2008-04-19Version 2
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.
Comments: 17 pages, to appear in Commun. Contemp. Math
A state-sum formula for the Alexander polynomial
A topological interpretation of Viro's $gl(1\vert 1)$-Alexander polynomial of a graph
On the Characterization Problem of Alexander Polynomials of Closed 3-Manifolds
![QR code for arXiv:0711.2836 [math.GT]](http://oss.arxitics.com/images/favicon.svg)