Homogeneous links, Seifert surfaces, digraphs and the reduced Alexander polynomial

Jessica E. Banks

doi:10.1007/s10711-012-9786-1

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arXiv · 1101.1412

Homogeneous links, Seifert surfaces, digraphs and the reduced Alexander polynomial

Jessica E. Banks

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Abstract

We give a geometric proof of the following result of Juhasz. \emph{Let $a_g$ be the leading coefficient of the Alexander polynomial of an alternating knot $K$. If $|a_g|<4$ then $K$ has a unique minimal genus Seifert surface.} In doing so, we are able to generalise the result, replacing `minimal genus' with `incompressible' and `alternating' with `homogeneous'. We also examine the implications of our proof for alternating links in general.

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Jessica E. Banks. 2011-01-07. Homogeneous links, Seifert surfaces, digraphs and the reduced Alexander polynomial. https://doi.org/10.1007/s10711-012-9786-1

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