Bohr Density of Simple Linear Group Orbits

TL;DR

This paper proves that nonzero orbits of certain simple linear groups are dense in the Bohr compactification, revealing a deep connection between group actions and topological compactifications.

Contribution

It establishes a new density result for orbits of noncompact simple linear groups in the Bohr compactification of the space.

Findings

Nonzero orbits are dense in the Bohr compactification.

The result applies to noncompact, simple, irreducible linear groups.

Provides insight into the structure of group actions on topological compactifications.

Abstract

We show that any nonzero orbit under a noncompact, simple, irreducible linear group is dense in the Bohr compactification of the ambient space.