A note on unavoidable sets for a spherical curve of reductivity four

Kenji Kashiwabara; Ayaka Shimizu

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arXiv · 1705.02450

A note on unavoidable sets for a spherical curve of reductivity four

Kenji Kashiwabara·Ayaka Shimizu

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Abstract

The reductivity of a spherical curve is the minimal number of a local transformation called an inverse-half-twisted splice required to obtain a reducible spherical curve from the 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 the question by constructing such a spherical curve.

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Kenji Kashiwabara, Ayaka Shimizu. 2017-05-06. A note on unavoidable sets for a spherical curve of reductivity four. https://arxiv.org/abs/1705.02450

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