JournalscmhVol. 95, No. 1pp. 37–78

Quasi-isometric embeddings of non-uniform lattices

  • David Fisher

    Indiana University, Bloomington, USA
  • Thang Nguyen

    Indiana University, Bloomington, USA
Quasi-isometric embeddings of non-uniform lattices cover

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Abstract

Let GG and GG' be simple Lie groups of equal real rank and real rank at least 22. Let Γ<G\Gamma <G and Λ<G\Lambda < G' be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of Γ\Gamma into Λ\Lambda is at bounded distance from a homomorphism. For example, any quasi-isometric embedding of SL(n,Z)SL(n,\mathbb Z) into SL(n,Z[i])SL(n, \mathbb 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.

Cite this article

David Fisher, Thang Nguyen, Quasi-isometric embeddings of non-uniform lattices. Comment. Math. Helv. 95 (2020), no. 1, pp. 37–78

DOI 10.4171/CMH/480