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The Auslander conjecture for NIL-affine crystallographic groups

Dietrich Burde·Karel Dekimpe·Sandra Deschamps
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Abstract

Let N be a simply connected, connected real nilpotent Lie group of finite dimension n. We study subgroups $Γ$ in $\Aff (N)=N\rtimes \Aut (N)$ acting properly discontinuously and cocompactly on N. This situation is a natural generalization of the so-called affine crystallographic groups. We prove that for all dimensions $1\le n\le 5$ the generalized Auslander conjecture holds, i.e., that such subgroups are virtually polycyclic.

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Dietrich Burde, Karel Dekimpe, Sandra Deschamps. 2004-09-24. The Auslander conjecture for NIL-affine crystallographic groups. https://arxiv.org/abs/math/0409476

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