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

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

2012-04-18

arxiv.org/abs/1204.4193v2

Mathematics

Geometric Topology

13 pages, 2 figures

Scientific paper

We prove that if $G$ is a non-uniform lattice in a rank-one semi-simple Lie
group $\ne Isom(\H^2_\R)$ then $G$ is quasi-isometrically co-Hopf. This means
that every quasi-isometric embedding $G\to G$ is coarsely onto and thus is a
quasi-isometry.

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