English

The Auslander conjecture for dimension less then 7

Group Theory 2020-11-26 v1

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.

Keywords

Cite

@article{arxiv.2011.12788,
  title  = {The Auslander conjecture for dimension less then 7},
  author = {H. Abels and G. A. Margulis and G. A. Soifer},
  journal= {arXiv preprint arXiv:2011.12788},
  year   = {2020}
}

Comments

55 pages. arXiv admin note: substantial text overlap with arXiv:1211.2525

R2 v1 2026-06-23T20:30:21.765Z