Abstract
In this paper we study the dynamics of properly discontinuous and crystallographic affine groups leaving a quadratic from of signature (p, q) invariant. The main results are: (I) If p − q ≥ 2, then the linear part of the group is not Zariski dense in the corresponding orthogonal group. (II) If q = 2 and the group is crystallographic, then the group is virtually solvable. This proves the Auslander conjecture for this case.
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Abels, H., Margulis, G.A. & Soifer, G.A. The linear part of an affine group acting properly discontinuously and leaving a quadratic form invariant. Geom Dedicata 153, 1–46 (2011). https://doi.org/10.1007/s10711-010-9554-z
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DOI: https://doi.org/10.1007/s10711-010-9554-z