Properly discontinuous groups of affine transformations with orthogonal linear part

Herbert Abels; Grigori A. Margulis; Grigori A. Soifer

doi:10.1016/S0764-4442(99)80356-5

Properly discontinuous groups of affine transformations with orthogonal linear part

Translated title of the contribution: Properly discontinuous groups of affine transformations with orthogonal linear part

Herbert Abels
, Grigori A. Margulis
, Grigori A. Soifer

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

Let Γ be a subgroup of the group of all affine transformations of a real affine space A of finite dimension. Suppose that Γ acts properly discontinuously on A. We determine which orthogonal groups can occur as Zariski closures of the linear part of Γ. Our methods yield a proof of Auslander's conjecture for affine spaces of dimension at most 6.

Translated title of the contribution	Properly discontinuous groups of affine transformations with orthogonal linear part
Original language	English
Pages (from-to)	253-258
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	324
Issue number	3
DOIs	https://doi.org/10.1016/S0764-4442(99)80356-5
State	Published - Feb 1997

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abstract = "Let Γ be a subgroup of the group of all affine transformations of a real affine space A of finite dimension. Suppose that Γ acts properly discontinuously on A. We determine which orthogonal groups can occur as Zariski closures of the linear part of Γ. Our methods yield a proof of Auslander's conjecture for affine spaces of dimension at most 6.",

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AB - Let Γ be a subgroup of the group of all affine transformations of a real affine space A of finite dimension. Suppose that Γ acts properly discontinuously on A. We determine which orthogonal groups can occur as Zariski closures of the linear part of Γ. Our methods yield a proof of Auslander's conjecture for affine spaces of dimension at most 6.

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Properly discontinuous groups of affine transformations with orthogonal linear part

Abstract

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