2007/12/06 by A. Stoimenow, Stoimenow, A.
Mathematics · #57M12 #57M25 (Primary) #57M50 (Secondary) #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M12 #msc:57M25 #msc:57M50
paper · pdf · doi:10.48550/arxiv.0712.0866
31 pages
arxiv created 2007/12/06 · openalex publication_date 2007/12/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.