2017/05/06 by Kenji Kashiwabara, Kashiwabara, Kenji, Ayaka Shimizu +1
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1705.02450
openalex publication_date 2017/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.