East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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REVISIT TO ALEXANDER MODULES OF 2-GENERATOR KNOTS IN THE 3-SPHERE

  • Song, Hyun-Jong (Department of Applied Mathematics, Pukyong National University)
  • Received : 2019.10.28
  • Accepted : 2020.04.15
  • Published : 2020.05.31
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Abstract

It is known that a 2-generator knot K has a cyclic Alexander module ℤ[t, t―1]/(Δ(t)) where Δ(t) is the Alexander polynomial of K. In this paper we explicitly show how to reduce 2-generator Alexander modules to cyclic ones by using Chiswell, Glass and Wilsons presentations of 2-generator knot groups $$<\;x,\;y\;{\mid}\;(x^{{\alpha}_1})^{y^{{\gamma}_1}},\;{\cdots}\;,\;(x^{{\alpha}_k})^{y^{{\gamma}_k}}\;>$$ where ab = bab-1.

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References

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