Properly discontinuous group actions on affine homogeneous spaces

TL;DR

This paper proves a generalized version of the Auslander conjecture for certain affine homogeneous spaces, specifically when the acting group's Levi factor has low rank or the space's dimension is at most five.

Contribution

It extends the Auslander conjecture to new cases involving low-rank Levi factors and low-dimensional spaces.

Findings

Proved the conjecture for Levi factors with simple real algebraic groups of rank ≤ 1.

Confirmed the conjecture for dimensions ≤ 5.

Generalized the conjecture beyond previous known cases.

Abstract

A generalization of the Auslander conjecture is proved in the case when the Levi factor of the Zariski closure of the acting group is a product of simple real algebraic groups of rank \leq 1. Also, the Auslander conjecture is proved for dimensions \leq 5.