Topological Symmetries of R^3

TL;DR

This paper proves that any finite group acting faithfully and orientation-preservingly on three-dimensional Euclidean space is isomorphic to a subgroup of the rotation group SO(3).

Contribution

It establishes a classification result linking topological symmetries in R^3 to classical rotational symmetries.

Findings

Finite groups acting on R^3 are subgroups of SO(3)

Topological, faithful, orientation-preserving actions correspond to classical symmetries

Provides a topological characterization of rotational symmetry groups

Abstract

If a finite group acts topologically, faithfully and orientation preservingly on R^3, then it is isomorphic to a subgroup of SO(3).