On the Colored Jones Polynomial and the Kashaev invariant

Details On the Colored Jones Polynomial and the Kashaev invariant On the Colored Jones Polynomial and the Kashaev invariant

2005-03-15

arxiv.org/abs/math/0503296v1

Mathematics

Geometric Topology

14 pages

Scientific paper

We express the colored Jones polynomial as the inverse of the quantum determinant of a matrix with entries in the $q$-Weyl algebra of $q$-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.

Affiliated with

Also associated with

No associations

Rating

On the Colored Jones Polynomial and the Kashaev invariant does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Colored Jones Polynomial and the Kashaev invariant, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Colored Jones Polynomial and the Kashaev invariant will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-316454