Volume 6, issue 2 (2006)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Euclidean Mahler measure and twisted links

Daniel S Silver, Alexander Stoimenow and Susan G Williams

Algebraic & Geometric Topology 6 (2006) 581–602

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 2000
Primary: 57M25
Secondary: 37B40
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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