On the orbit space of a three-dimensional compact linear Lie group

TL;DR

This paper investigates when the quotient space of a real linear representation of a 3D compact Lie group forms a manifold, providing bounds and analyzing specific cases to understand the topological structure.

Contribution

It establishes an upper bound on the dimension of representations with manifold quotients and examines various remaining cases for simple three-dimensional compact Lie groups.

Findings

Derived an upper bound for representation dimensions with manifold quotients

Analyzed specific cases of 3D compact Lie group representations

Identified conditions under which the quotient is a manifold

Abstract

We study the question of whether the topological quotient of a real linear representation of a simple three-dimensional compact Lie group is a manifold. We obtain an upper bound for the dimension of a representation whose quotient is a manifold, and examine most of the remaining cases.