Euclidean Mahler measure and twisted links

Details Euclidean Mahler measure and twisted links Euclidean Mahler measure and twisted links

2004-12-28

arxiv.org/abs/math/0412513v4

Algebr. Geom. Topol. 6 (2006) 581-602

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 7 April 2006

Scientific paper

10.2140/agt.2006.6.581

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.

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