Euclidean Mahler measure and twisted links

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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Keywords

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

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 37B40

References

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Publication

Received: 26 March 2005

Accepted: 15 March 2006

Published: 7 April 2006

Authors

Daniel S Silver
Department of Mathematics and Statistics University of South Alabama Mobile, AL 36688-0002 USA

Alexander Stoimenow
Graduate School of Mathematical Sciences University of Tokyo 3-8-1, Komaba Tokyo 153-8914 Japan

Susan G Williams
Department of Mathematics and Statistics University of South Alabama Mobile, AL 36688-0002 USA

Volume 6, issue 2 (2006)

Daniel S Silver, Alexander Stoimenow and Susan G Williams

Abstract