Algebraic & Geometric Topology 6 (2006) 581–602

DOI: 10.2140/agt.2006.6.581

arXiv: math.GT/0412513

Abstract

If the twist numbers of a collection of oriented alternating link diagrams are bounded, then the Alexander polynomials of the corresponding links have bounded euclidean Mahler measure (see Definition 1.2). The converse assertion does not hold. Similarly, if a collection of oriented link diagrams, not necessarily alternating, have bounded twist numbers, then both the Jones polynomials and a parametrization of the 2–variable Homflypt polynomials of the corresponding links have bounded Mahler measure.

Keywords

link, twist number, Alexander polynomial, Jones polynomial, Mahler measure

Mathematical Subject Classification

Primary: 57M25

Secondary: 37B40

References

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Publication

Received: 26 March 2005
Accepted: 15 March 2006
Published: 7 April 2006

Authors