Coarse differentiation and quasi-isometries of a class of solvable Lie groups. I. (Q640349)

It is often conjectured that the subclass of polycyclic groups form a quasi-isometrically rigid class. The main theorem here characterizes a quasi-isometry \(\phi:G \to G'\), where \(G,G'\) are nondegenerate, unimodular, split abelian-by-abelian Lie groups. A description of the geometry of nondegenerate split abelian-by-abelian group is given.