On links with cyclotomic Jones polynomials
Geometric Topology
2009-04-30 v3
Abstract
We show that if {L_n} is any infinite sequence of links with twist number tau(L_n) and with cyclotomic Jones polynomials of increasing span, then lim sup tau(L_n)=infty. This implies that any infinite sequence of prime alternating links with cyclotomic Jones polynomials must have unbounded hyperbolic volume. The main tool is the multivariable twist--bracket polynomial, which generalizes the Kauffman bracket to link diagrams with open twist sites.
Keywords
Cite
@article{arxiv.math/0605631,
title = {On links with cyclotomic Jones polynomials},
author = {Abhijit Champanerkar and Ilya Kofman},
journal= {arXiv preprint arXiv:math/0605631},
year = {2009}
}
Comments
This is the version published by Algebraic & Geometric Topology on 14 October 2006