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Free totally discontinuous groups of affine transformations. (English. Russian original) Zbl 0578.57012

Sov. Math., Dokl. 28, 435-439 (1983); translation from Dokl. Akad. Nauk SSSR 272, 785-788 (1983).
The Milnor conjecture (the fundamental group of any complete affine variety is almost polycyclic) may be formulated in the following equivalent form: any subgroup of the affine transformation group A(n) which acts totally discontinuously on \({\mathbb{R}}^ n\) is almost polycyclic (i.e. contains a polycyclic subgroup of finite index).
In this note it is proved that for \(n=3\) the answer to this conjecture is negative.
Reviewer: A.Neagu

MSC:

57S30 Discontinuous groups of transformations
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
22E40 Discrete subgroups of Lie groups
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