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On links with cyclotomic Jones polynomials

Abhijit Champanerkar, Ilya Kofman

math.GTarXiv:math/0605631

Abstract

We show that if Ln is any infinite sequence of links with twist number tau(Ln) and with cyclotomic Jones polynomials of increasing span, then lim sup tau(Ln)=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.

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