The reductivity of spherical curves Part II: 4-gons

TL;DR

This paper investigates the reductivity of spherical curves, specifically focusing on 4-gons, and provides an unavoidable set for curves with reductivity four, advancing understanding of their structural properties.

Contribution

It introduces an unavoidable set for spherical curves with reductivity four by analyzing 4-gons, addressing an open question in the field.

Findings

Identifies an unavoidable set for spherical curves with reductivity four.

Provides structural insights into 4-gons within spherical curves.

Advances the classification of spherical curves based on reductivity.

Abstract

The reductivity of a spherical curve represents how reduced the spherical curve is. It is unknown if there exists a spherical curve whose reductivity is four. In this paper we give an unavoidable set for spherical curves with reductivity four by considering 4-gons.