The Auslander conjecture for NIL-affine crystallographic groups

Burde, Dietrich; Dekimpe, Karel; Deschamps, Sandra

The Auslander conjecture for NIL-affine crystallographic groups

Authors

Burde, Dietrich

Dekimpe, Karel

Deschamps, Sandra

Description

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.
14 pages