On the Head and the Tail of the Colored Jones Polynomial
Geometric Topology
2007-05-23 v1 Quantum Algebra
Abstract
The colored Jones polynomial is a series of one variable Laurent polynomials J(K,n) associated with a knot K in 3-space. We will show that for an alternating knot K the absolute values of the first and the last three leading coefficients of J(K,n) are independent of n when n is sufficiently large. Computation of sample knots indicates that this should be true for any fixed leading coefficient of the colored Jones polynomial for alternating knots. As a corollary we get a Volume-ish Theorem for the colored Jones Polynomial.
Keywords
Cite
@article{arxiv.math/0604230,
title = {On the Head and the Tail of the Colored Jones Polynomial},
author = {Oliver T. Dasbach and Xiao-Song Lin},
journal= {arXiv preprint arXiv:math/0604230},
year = {2007}
}
Comments
14 pages, 6 figures