On the Colored Jones Polynomial and the Kashaev invariant
Geometric Topology
2007-05-23 v1 Quantum Algebra
Abstract
We express the colored Jones polynomial as the inverse of the quantum determinant of a matrix with entries in the -Weyl algebra of -operators, evaluated at the trivial function (plus simple substitutions). The Kashaev invariant is proved to be equal to another special evaluation of the determinant. We also discuss the similarity between our determinant formula of the Kashaev invariant and the determinant formula of the hyperbolic volume of knot complements, hoping it would lead to a proof of the volume conjecture.
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Cite
@article{arxiv.math/0503296,
title = {On the Colored Jones Polynomial and the Kashaev invariant},
author = {Vu Huynh and Thang T. Q. Le},
journal= {arXiv preprint arXiv:math/0503296},
year = {2007}
}
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14 pages