## Geometry & Topology

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

Irine Peng

#### Abstract

This is the first of two consecutive papers that aim to understand quasi-isometries of a class of unimodular split solvable Lie groups. In the present paper, we show that locally (in a coarse sense), a quasi-isometry between two groups in this class is close to a map that respects their group structures. In the following paper we will use this result to show quasi-isometric rigidity.

#### Article information

Source
Geom. Topol., Volume 15, Number 4 (2011), 1883-1925.

Dates
Revised: 3 August 2011
Accepted: 3 August 2011
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732357

Digital Object Identifier
doi:10.2140/gt.2011.15.1883

Mathematical Reviews number (MathSciNet)
MR2860983

Zentralblatt MATH identifier
1235.51019

#### Citation

Peng, Irine. Coarse differentiation and quasi-isometries of a class of solvable Lie groups I. Geom. Topol. 15 (2011), no. 4, 1883--1925. doi:10.2140/gt.2011.15.1883. https://projecteuclid.org/euclid.gt/1513732357

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