2005/06/29 by Eriko Hironaka, Hironaka, Eriko · 2 citations
Mathematics · #57M25 #57M50 (primary) 11R06 (secondary) #Advanced Combinatorial Mathematics #Alexander polynomial #Algebraic structures and combinatorial models #Combinatorics #Discrete mathematics #FOS: Mathematics #Fibered knot #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homology (biology) #Iterated function #Knot (papermaking) #Knot theory #Mathematical analysis #Mathematics #Monodromy #Polynomial #Pure mathematics #Sequence (biology) #math.GT #msc:11R06 #msc:57M25 #msc:57M50
paper · pdf · doi:10.48550/arxiv.math/0506602
18 pages, 6 figures, to appear in Osaka J. Math
arxiv created 2005/06/29 · openalex publication_date 2005/06/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Given a fibered link, consider the characteristic polynomial of the monodromy restricted to first homology. This generalizes the notion of the Alexander polynomial of a knot. We define a construction, called iterated plumbing, to create a sequence of fibered links from a given one. The resulting sequence of characteristic polynomials has the same form as those arising in work of Salem and Boyd in their study of distributions of Salem and P-V numbers. From this we deduce information about the asymptotic behavior of the large roots of the generalized Alexander polynomials, and define a new poset structure for Salem fibered links.