On links with cyclotomic Jones polynomials

Details On links with cyclotomic Jones polynomials On links with cyclotomic Jones polynomials

2006-05-23

arxiv.org/abs/math/0605631v3

Algebr. Geom. Topol. 6 (2006) 1655-1668

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 14 October 2006

Scientific paper

10.2140/agt.2006.6.1655

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.

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