[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2019.59.4.821

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)

Publication Information

Kyungpook Mathematical Journal / v.59, no.4, 2019 , pp. 821-834 More about this Journal

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.

Keywords

knot projection; reductivity; spherical curve; unavoidable set;

Citations & Related Records

Reference

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