Affine action and Margulis invariant
For a complete flat affine manifold \(M\), Milnor has conjectured that the fundamental group \({\pi}_1(M)\) is virtually polycyclic. In this paper the author shows that two Zariski dense subgroups consisting of hyperbolic elements of \(\text{SO}(n+1,n)\times{\mathbb R}^{2n+1}\) with the same Margulis invariant are conjugated (Theorem A). The author studies the Margulis invariant and shows that this invariant completely determines the affine action up to translational conjugacy. He also considers in affine deformations an analogue of quasi-Fuchsian deformations of Fuchsian groups.
scientific article; zbMATH DE number 2141624
scientific article