Abstract
Let G and G' be simple Lie groups of equal real rank and real rank at least 2 . Let \Gamma <G and \Lambda < G' be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of \Gamma into \Lambda is at bounded distance from a homomorphism. For example, any quasi-isometric embedding of SL(n,\mathbb Z) into SL(n, \mathbb Z[i]) is at bounded distance from a homomorphism. We also include a discussion of some cases when this result is not true for what turn out to be purely algebraic reasons.
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