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The Auslander conjecture for dimension less then 7

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arxiv 2011.12788 v1 pith:6XKPSMZW submitted 2020-11-24 math.GR

H. Abels , G.A. Margulis , G.A. Soifer This is my paper · ORCID
classification math.GR
keywords auslanderconjectureargumentscohomologicalproofsolvablesubgroupaffine
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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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  1. Topological volumes of certain complete affine manifolds

    math.GT 2025-02 accept novelty 6.0 of 10

    Complete affine manifolds with an infinite amenable normal subgroup have amenable category at most their dimension, so all three topological volumes vanish.

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