The Configuration Space of n-Tuples of Equiangular Unit Vectors for n=3, 4, and 5

Yasuhiko Kamiyama

doi:10.1155/2018/9842324

Abstract

Let Mn(θ) be the configuration space of n-tuples of unit vectors in R3 such that all interior angles are θ. The space Mn(θ) is an (n-3)-dimensional space. This paper determines the topological type of Mn(θ) for n=3, 4, and 5.

Highlights

Starting in [1], the topology of the configuration space of spatial polygons of arbitrary edge lengths has been considered by many authors
Crippen [8] studied the topological type of Xn(θ) for n = 3, 4, and 5
The purpose of this paper is to determine the topological type of Mn(θ) for n = 3, 4, and 5

Summary

Introduction

Starting in [1], the topology of the configuration space of spatial polygons of arbitrary edge lengths has been considered by many authors. Many topological properties of Pn(l) are already known: First, it is clear that there is a homeomorphism We consider the space of n-tuples of equiangular unit vectors in R3. We define the following: We fix θ ∈ [0, π] and set

Objectives

Results

Conclusion