Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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A Note on Unavoidable Sets for a Spherical Curve of Reductivity Four

  • Kashiwabara, Kenji (Department of General Systems Studies, University of Tokyo) ;
  • Shimizu, Ayaka (Department of Mathematics, National Institute of Technology)
  • Received : 2018.10.11
  • Accepted : 2019.03.18
  • Published : 2019.12.23
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Abstract

The reductivity of a spherical curve is the minimal number of times a particular local transformation called an inverse-half-twisted splice is required to obtain a reducible spherical curve from the initial spherical curve. It is unknown if there exists a spherical curve whose reductivity is four. In this paper, an unavoidable set of configurations for a spherical curve with reductivity four is given by focusing on 5-gons. It has also been unknown if there exists a reduced spherical curve which has no 2-gons and 3-gons of type A, B and C. This paper gives the answer to this question by constructing such a spherical curve.

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References

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