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The second coefficient of the Alexander polynomial as a satellite obstruction

2024/02/05 by Lukas Lewark, Lewark, Lukas
Mathematics · Physics and Astronomy · #57K10 #57K14 #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Theories and Applications #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2402.03155

openalex publication_date 2024/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A set L of links is introduced, containing positive braid links as well as arborescent positive Hopf plumbings. 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.

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