{"paper":{"title":"Quasi-isometric embeddings of non-uniform lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GR","authors_text":"David Fisher, Thang Nguyen","submitted_at":"2015-12-22T22:32:51Z","abstract_excerpt":"Let $G$ and $G'$ be simple Lie groups of equal real rank and real rank at least $2$. Let $\\Gamma <G$ and $\\Lambda < G'$ be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of $\\Gamma$ into $\\Lambda$ is at bounded distance from a homomorphism. For example, any quasi-isometric embedding of $SL(n,\\mathbb Z)$ into $SL(n, \\mathbb Z[i])$ 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07285","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}