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

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

2011-01-07

arxiv.org/abs/1101.1412v2

Mathematics

Geometric Topology

37 pages, 28 figures; v2 Main results generalised from alternating links to homogeneous links. Title changed

Scientific paper

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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