{"paper":{"title":"Quasi-isometry of pairs: surfaces in graph manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Hoang Thanh Nguyen","submitted_at":"2018-08-08T11:03:17Z","abstract_excerpt":"We show there exists a closed graph manifold $N$ and infinitely many non-separable, horizontal surfaces $\\{S_{n} \\to N\\}_{n \\in \\mathbb{N}}$ such that there does not exist a quasi-isometry $\\pi_1(N) \\to \\pi_1(N)$ taking $\\pi_1(S_{n})$ to $\\pi_1(S_{m})$ within a finite Hausdorff distance when $n \\neq m$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02722","kind":"arxiv","version":1},"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"}