Euclidean Mahler measure and twisted links

Silver, Daniel S¹ ; Stoimenow, Alexander² ; Williams, Susan G¹

¹Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688-0002, USA
²Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1, Komaba, Tokyo 153-8914, Japan

Algebraic and Geometric Topology, Tome 6 (2006) no. 2, pp. 581-602

Résumé

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.

Détail

DOI : 10.2140/agt.2006.6.581

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

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