ar X iv : 1 51 2 . 07 28 5 v 2 [ m at h . G R ] 2 2 M ay 2 01 7 QUASI - ISOMETRIC EMBEDDINGS OF NON - UNIFORM LATTICES
نویسنده
چکیده
Let G and G be simple Lie groups of equal real rank and real rank at least 2. Let Γ < G and Λ < G be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of Γ into Λ is at bounded distance from a homomorphism. For example, any quasiisometric 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.
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