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

Jessica E. Banks

doi:10.1007/s10711-012-9786-1

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

Geometric Topology 2018-07-17 v2

Authors: 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.

Keywords

homogeneous links Seifert surfaces digraphs reduced Alexander polynomial alternating knots incompressible surfaces minimal genus

Cite

@article{arxiv.1101.1412,
  title  = {Homogeneous links, Seifert surfaces, digraphs and the reduced Alexander polynomial},
  author = {Jessica E. Banks},
  journal= {arXiv preprint arXiv:1101.1412},
  year   = {2018}
}

Comments

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

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

Abstract

Keywords

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