Antipodal Point Arrangements on Spheres and Classification of Normal Systems

TL;DR

This paper classifies antipodal point arrangements on spheres of any dimension using cycle invariants, providing a systematic way to distinguish different configurations.

Contribution

It introduces a novel classification method for antipodal arrangements on spheres based on finite cycle invariants, extending understanding of geometric configurations.

Findings

Complete classification of antipodal arrangements on spheres

Introduction of cycle invariants as classification tools

Framework applicable to all dimensions greater than one

Abstract

For any positive integer $k>1$, we classify the antipodal point arrangements on the sphere $S^k$ up to an isomorphism, by associating a finite complete set of cycle invariants.