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2006 On links with cyclotomic Jones polynomials
Abhijit Champanerkar, Ilya Kofman
Algebr. Geom. Topol. 6(4): 1655-1668 (2006). DOI: 10.2140/agt.2006.6.1655

Abstract

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

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Abhijit Champanerkar. Ilya Kofman. "On links with cyclotomic Jones polynomials." Algebr. Geom. Topol. 6 (4) 1655 - 1668, 2006. https://doi.org/10.2140/agt.2006.6.1655

Information

Received: 5 June 2006; Accepted: 28 August 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1130.57006
MathSciNet: MR2253460
Digital Object Identifier: 10.2140/agt.2006.6.1655

Subjects:
Primary: 57M25
Secondary: 26C10

Rights: Copyright © 2006 Mathematical Sciences Publishers

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