Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4582509 | Expositiones Mathematicae | 2010 | 46 Pages |
Abstract
We realize a given (monic) Alexander polynomial by a (fibered) hyperbolic arborescent knot and link having any number of components, and by infinitely many such links having at least 4 components. As a consequence, a Mahler measure minimizing polynomial, if it exists, is realized as the Alexander polynomial of a fibered hyperbolic link of at least 2 components. For a given polynomial, we also give an upper bound for the minimal hyperbolic volume of knots/links realizing the polynomial and, in the opposite direction, construct knots of arbitrarily large volume, which are arborescent, or have given free genus at least 2.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
A. Stoimenow,