The Auslander conjecture for dimension less then 7

2020/11/24 by Abels, H., Margulis, G. A., Soifer, G. A.
#22E40 #37B02 #F.2.2 #FOS: Mathematics #Group Theory (math.GR) #I.2.7

paper · doi:10.48550/arxiv.2011.12788

Abstract

In 1964 L. Auslander conjectured that every crystallographic subgroup of an the affine group is virtually solvable, i.e. contains a solvable subgroup of finite index. D. Fried and W. Goldman proved Auslander's conjecture for n = 3 using cohomological arguments. We prove the Auslander conjecture for n < 7. The proof is based mainly on dynamical arguments. In some cases, we use the cohomological argument which we could avoid but it would significantly lengthen the proof.

Related

• The Auslander conjecture for dimension less than 7
• The Auslander conjecture for NIL-affine crystallographic groups
• Properly discontinuous group actions on affine homogeneous spaces
• The Herzog-Schönheim conjecture for solvable groups
• Noncommutative Auslander theorem