| 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 Lambda into Gamma is at bounded distance from a homomorphism. For example, any quasi-isometric embedding of SL(n, Z) into SL(n, 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. |
