Geometry & Topology

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

Irine Peng

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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.

Article information

Source
Geom. Topol., Volume 15, Number 4 (2011), 1927-1981.

Dates
Received: 13 April 2009
Revised: 3 August 2011
Accepted: 3 August 2011
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732358

Digital Object Identifier
doi:10.2140/gt.2011.15.1927

Mathematical Reviews number (MathSciNet)
MR2860984

Zentralblatt MATH identifier
1242.51008

Subjects
Primary: 51F99: None of the above, but in this section
Secondary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]

Keywords
quasi-isometry solvable group rigidity

Citation

Peng, Irine. Coarse differentiation and quasi-isometries of a class of solvable Lie groups II. Geom. Topol. 15 (2011), no. 4, 1927--1981. doi:10.2140/gt.2011.15.1927. https://projecteuclid.org/euclid.gt/1513732358


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