{"paper":{"title":"Linear and projective boundaries in HNN-extensions and distortion phenomena","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Bernhard Kr\\\"on, J\\\"org Lehnert, Maya Stein","submitted_at":"2012-10-15T18:52:40Z","abstract_excerpt":"Linear and projective boundaries of Cayley graphs were introduced in~\\cite{kst} as quasi-isometry invariant boundaries of finitely generated groups. They consist of forward orbits $g^\\infty=\\{g^i: i\\in \\mathbb N\\}$, or orbits $g^{\\pm\\infty}=\\{g^i:i\\in\\mathbb Z\\}$, respectively, of non-torsion elements~$g$ of the group $G$, where `sufficiently close' (forward) orbits become identified, together with a metric bounded by 1.\n  We show that for all finitely generated groups, the distance between the antipodal points $g^\\infty$ and $g^{-\\infty}$ in the linear boundary is bounded from below by $\\sqrt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4137","kind":"arxiv","version":4},"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"}