Algebraic & Geometric Topology 6 (2006) 1655–1668

DOI: 10.2140/agt.2006.6.1655

arXiv: math.GT/0605631

Abstract

We show that if {L_n} is any infinite sequence of links with twist number τ(L_n) and with cyclotomic Jones polynomials of increasing span, then lim sup τ(L_n)=∞. 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

Jones polynomial, Mahler measure, twist sites, hyperbolic volume

Mathematical Subject Classification

Primary: 57M25

Secondary: 26C10

References

Publication

Received: 5 June 2006
Accepted: 28 August 2006
Published: 14 October 2006

Authors