On links with cyclotomic Jones polynomials
arXiv:math/0605631 · doi:10.2140/agt.2006.6.1655
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.
This is the version published by Algebraic & Geometric Topology on 14 October 2006