Quasi-isometries of rank one S-arithmetic lattices

Kevin Wortman

Published 2005-04-11, updated 2008-01-08Version 2

We complete the quasi-isometric classification of irreducible lattices in semisimple Lie groups over nondiscrete locally compact fields of characteristic zero by showing that any quasi-isometry of a rank one S-arithmetic lattice in a semisimple Lie group over nondiscrete locally compact fields of characteristic zero is a finite distance in the sup-norm from a commensurator.