Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Quantization of the Crossing Number of a Knot Diagram

  • KAWAUCHI, AKIO (Osaka City University Advanced Mathematical Institute) ;
  • SHIMIZU, AYAKA (Department of Mathematics, Gunma National College of Technology)
  • Received : 2014.01.28
  • Accepted : 2014.07.14
  • Published : 2015.09.23
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Abstract

We introduce the warping crossing polynomial of an oriented knot diagram by using the warping degrees of crossing points of the diagram. Given a closed transversely intersected plane curve, we consider oriented knot diagrams obtained from the plane curve as states to take the sum of the warping crossing polynomials for all the states for the plane curve. As an application, we show that every closed transversely intersected plane curve with even crossing points has two independent canonical orientations and every based closed transversely intersected plane curve with odd crossing points has two independent canonical orientations.

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References

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Cited by

  1. The rank of a warping matrix vol.206, 2016, https://doi.org/10.1016/j.topol.2016.04.003
  2. On the orientations of monotone knot diagrams vol.26, pp.10, 2017, https://doi.org/10.1142/S0218216517500535