The Auslander conjecture for NIL-affine crystallographic groups

Details The Auslander conjecture for NIL-affine crystallographic groups The Auslander conjecture for NIL-affine crystallographic groups

2004-09-24

arxiv.org/abs/math/0409476v1

Math. Ann. 332, No. 1, 161--176 (2005)

Mathematics

Differential Geometry

14 pages

Scientific paper

Let N be a simply connected, connected real nilpotent Lie group of finite dimension n. We study subgroups $\Gamma$ 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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