A note on unavoidable sets for a spherical curve of reductivity four
Geometric Topology
2018-10-12 v3
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.
Cite
@article{arxiv.1705.02450,
title = {A note on unavoidable sets for a spherical curve of reductivity four},
author = {Kenji Kashiwabara and Ayaka Shimizu},
journal= {arXiv preprint arXiv:1705.02450},
year = {2018}
}
Comments
16 pages, 22 figures