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

Peng, Irine

doi:10.2140/gt.2011.15.1883

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

Irine Peng

Geometry & Topology 15 (2011) 1883–1925

DOI: 10.2140/gt.2011.15.1883

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

Volume 15, issue 4 (2011)