On the zariski closure of the linear part of a properly discontinuous group of affine transformations

H. Abels, G. A. Margulis, G. A. Soifer

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Abstract

Let Γ be a subgroup of the group of affine transformations of the affine space ℝ2n+1. Suppose Γ acts properly discontinuously on ℝ2n+1. The paper deals with the question which subgroups of GL(2n+1,ℝ) occur as Zariski closure ℓ(Γ)¯ of the linear part of such a group Γ. The two main results of the paper say that SO(n + 1, n) does occur as ℓ(Γ)¯ of such a group Γ if n is odd, but does not if n is even.

Original languageEnglish
Pages (from-to)315-344
Number of pages30
JournalJournal of Differential Geometry
Volume60
Issue number2
DOIs
StatePublished - 2002

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