The Auslander conjecture for NIL-affine crystallographic groups

2004/09/24 by Dietrich Burde, Karel Dekimpe, Sandra Deschamps
Mathematics · #math.DG

paper · pdf

published as Math. Ann. 332, No. 1, 161--176 (2005) · 14 pages

arxiv created 2004/09/24 · arxiv updated 2009/12/01

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≤ n≤ 5 the generalized Auslander conjecture holds, i.e., that such subgroups are virtually polycyclic.

Related

• The Auslander conjecture for dimension less than 7
• The Auslander conjecture for dimension less then 7
• NIL-affine crystallographic actions of virtually polycyclic groups
• Properly discontinuous group actions on affine homogeneous spaces
• Special Lagrangian fibrations, Berkovich retraction, and crystallographic groups