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

Peng, Irine

doi:10.2140/gt.2011.15.1927

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

Irine Peng

Geometry & Topology 15 (2011) 1927–1981

DOI: 10.2140/gt.2011.15.1927

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

Volume 15, issue 4 (2011)