Coarse differentiation and quasi-isometries of a class of solvable Lie groups II

Details Coarse differentiation and quasi-isometries of a class of solvable Lie groups II Coarse differentiation and quasi-isometries of a class of solvable Lie groups II

2010-02-24

arxiv.org/abs/1002.4451v1

Mathematics

Metric Geometry

Scientific paper

In this paper, we continue with the results in \cite{Pg} and compute the group of quasi-isometries for a subclass of split solvable unimodular Lie groups. Consequently, we show that any finitely generated group quasi-isometric to a member of the subclass has to be polycyclic, and is virtually a lattice in an abelian-by-abelian solvable Lie group. We also give an example of a unimodular solvable Lie group that is not quasi-isometric to any finitely generated group, as well deduce some quasi-isometric rigidity results.

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