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

Kapovich, Ilya; Lukyanenko, Anton

doi:10.1090/S1088-4173-2012-00246-9

Quasi-isometric co-Hopficity of non-uniform lattices in rank-one semi-simple Lie groups
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by Ilya Kapovich and Anton Lukyanenko

Conform. Geom. Dyn. 16 (2012), 269-282

DOI: https://doi.org/10.1090/S1088-4173-2012-00246-9

Published electronically: October 15, 2012

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Abstract:

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

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