Alexander polynomials and hyperbolic volume of arborescent links
Geometric Topology
2007-12-07 v1
Abstract
We realize a given (monic) Alexander polynomial by a (fibered) hyperbolic arborescent knot and link of any number of components, and by infinitely many such links of 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 given polynomial, we give also an upper bound on the minimal hyperbolic volume of knots/links, and contrarily, construct knots of arbitrarily large volume, which are arborescent, or have given free genus at least 2.
Cite
@article{arxiv.0712.0866,
title = {Alexander polynomials and hyperbolic volume of arborescent links},
author = {A. Stoimenow},
journal= {arXiv preprint arXiv:0712.0866},
year = {2007}
}
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31 pages