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

Irine Peng

Geometry & Topology 15 (2011) 1883–1925
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.

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