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arXiv · 2011.12788

The Auslander conjecture for dimension less then 7

H. Abels·G. A. Margulis·G. A. Soifer
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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.

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H. Abels, G. A. Margulis, G. A. Soifer. 2020-11-24. The Auslander conjecture for dimension less then 7. https://arxiv.org/abs/2011.12788

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