The second coefficient of the Alexander polynomial as a satellite obstruction

A set P of links is introduced, containing positive braid links as well as arborescent positive Hopf plumbings. Inspired by work of Ito, it is shown that for links in P, the leading and the second coefficient of the Alexander polynomial have opposite sign. It follows that certain satellite links, su...

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Bibliographic Details
Published in:arXiv.org 2024-02
Main Author: Lewark, Lukas
Format: Article
Language:English
Subjects:
Cables
Links
Polynomials
Satellite communications
Online Access:Get full text
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Summary:A set P of links is introduced, containing positive braid links as well as arborescent positive Hopf plumbings. Inspired by work of Ito, it is shown that for links in P, the leading and the second coefficient of the Alexander polynomial have opposite sign. It follows that certain satellite links, such as (n,1)-cables, are not in P.
ISSN:2331-8422