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Euclidean Mahler measure
and twisted links
Daniel S Silver, Alexander Stoimenow and Susan G Williams |
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Algebraic & Geometric Topology 6 (2006) 581–602
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arXiv: math.GT/0412513 |
Abstract |
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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
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Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 37B40
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References |
Forward citations |
Publication
Received: 26 March 2005
Accepted: 15 March 2006
Published: 7 April 2006
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Authors |
| Daniel S Silver | |
| Department of Mathematics and
Statistics University of South Alabama Mobile, AL 36688-0002 USA |
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| Alexander Stoimenow | |
| Graduate School of Mathematical
Sciences University of Tokyo 3-8-1, Komaba Tokyo 153-8914 Japan |
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| Susan G Williams | |
| Department of Mathematics and
Statistics University of South Alabama Mobile, AL 36688-0002 USA |
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