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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Coarse differentiation and quasi-isometries of a class of solvable Lie groups II

Irine Peng

Geometry & Topology 15 (2011) 1927–1981
Abstract

In this paper, we continue with the results of the preceeding paper 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.

Keywords
quasi-isometry, solvable group, rigidity
Mathematical Subject Classification 2000
Primary: 51F99
Secondary: 22E40
References
Publication
Received: 13 April 2009
Revised: 3 August 2011
Accepted: 3 August 2011
Published: 17 October 2011
Proposed: Benson Farb
Seconded: Danny Calegari, Martin R Bridson
Authors
Irine Peng
Department of Mathematics
Indiana University
831 E 3rd St
Bloomington IN 47401
USA