Zeros of the Alexander polynomial of knot

The leading coefficient of the Alexander polynomial of a knot is the most informative element derived from this invariant, and the growth of orders of the first homology of cyclic branched covering spaces is also a familiar subject. Accordingly, there are a lot of investigations in each subject. How...

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Bibliographic Details
Published inOsaka Journal of Mathematics Vol. 44; no. 3; pp. 567 - 577
Main Author Noguchi, Akio
Format Journal Article
LanguageEnglish
Published Osaka University and Osaka City University, Departments of Mathematics 01.09.2007
Subjects
11S05
37B40
57M27
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ISSN0030-6126

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Summary:The leading coefficient of the Alexander polynomial of a knot is the most informative element derived from this invariant, and the growth of orders of the first homology of cyclic branched covering spaces is also a familiar subject. Accordingly, there are a lot of investigations in each subject. However, there is no study which deals with both subjects in the same context. In this paper, we show that the two subjects are closely related in p-adic number theory and dynamical systems.
ISSN:0030-6126