#### Volume 6, issue 4 (2006)

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On links with cyclotomic Jones polynomials

### Abhijit Champanerkar and Ilya Kofman

Algebraic & Geometric Topology 6 (2006) 1655–1668
 arXiv: math.GT/0605631
##### Abstract

We show that if $\left\{{L}_{n}\right\}$ is any infinite sequence of links with twist number $\tau \left({L}_{n}\right)$ and with cyclotomic Jones polynomials of increasing span, then $limsup\tau \left({L}_{n}\right)=\infty$. 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
Jones polynomial, Mahler measure, twist sites, hyperbolic volume
Primary: 57M25
Secondary: 26C10
##### Publication
Received: 5 June 2006
Accepted: 28 August 2006
Published: 14 October 2006
##### Authors
 Abhijit Champanerkar Department of Mathematics and Statistics University of South Alabama Mobile, AL 36688 USA Ilya Kofman Department of Mathematics College of Staten Island City University of New York 2800 Victory Boulevard Staten Island, NY 10314 USA