Geometry & Topology
- Geom. Topol.
- Volume 15, Number 4 (2011), 1883-1925.
Coarse differentiation and quasi-isometries of a class of solvable Lie groups I
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.
Geom. Topol., Volume 15, Number 4 (2011), 1883-1925.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 51F99: None of the above, but in this section
Secondary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
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