The quasi-isometry classification of rank one lattices

@article{Schwartz1995TheQC,
  title={The quasi-isometry classification of rank one lattices},
  author={Richard Evan Schwartz},
  journal={Publications Math{\'e}matiques de l'Institut des Hautes {\'E}tudes Scientifiques},
  year={1995},
  volume={82},
  pages={133-168}
}
  • R. Schwartz
  • Published 1995
  • Mathematics
  • Publications Mathématiques de l'Institut des Hautes Études Scientifiques
Let X be a symmetric space—other than the hyperbolic plane—of strictly negative sectional curvature. Let G be the isometry group of X. We show that any quasi-isometry between non-uniform lattices in G is equivalent to (the restriction of) a group element of G which commensurates one lattice to the other. This result has the following corollaries:1.Two non-uniform lattices in G are quasi-isometric if and only if they are commensurable.2.Let Γ be a finitely generated group which is quasi… 
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