Quasi-isometric co-Hopficity of non-uniform lattices in rank-one semi-simple Lie groups

@article{Kapovich2012QuasiisometricCO,
  title={Quasi-isometric co-Hopficity of non-uniform lattices in rank-one semi-simple Lie groups},
  author={Ilya Kapovich and Anton Lukyanenko},
  journal={Conformal Geometry and Dynamics of The American Mathematical Society},
  year={2012},
  volume={16},
  pages={269-282}
}
  • Ilya Kapovich, Anton Lukyanenko
  • Published 2012
  • Mathematics
  • Conformal Geometry and Dynamics of The American Mathematical Society
  • We prove that if G is a non-uniform lattice in a rank-one semi- simple Lie group 6 Isom(H 2 ) then G is quasi-isometrically co-Hopf. This means that every quasi-isometric embedding G → G is coarsely surjective and thus is a quasi-isometry. 

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 25 REFERENCES
    The quasi-isometry classification of rank one lattices
    114
    On Co-Hopfian Nilpotent Groups
    25
    A Sierpiński carpet with the co-Hopfian property
    20
    ENDOMORPHISMS OF HYPERBOLIC GROUPS I: THE HOPF PROPERTY
    62
    Embeddings of Gromov Hyperbolic Spaces
    279
    Quasi-isometric rigidity of nonuniform lattices in higher rank symmetric spaces
    51
    Structure and Rigidity in (Gromov) Hyperbolic Groups and Discrete Groups in Rank 1 Lie Groups II
    159
    COFINITELY HOPFIAN GROUPS, OPEN MAPPINGS AND KNOT COMPLEMENTS
    6
    Immeubles hyperboliques, dimension conforme et rigidité de Mostow
    137
    Endomorphisms of Relatively Hyperbolic Groups
    16