{"paper":{"title":"Bounded Depth Ascending HNN Extensions and $\\pi_1$-Semistability at $\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Michael Mihalik","submitted_at":"2017-09-26T17:24:06Z","abstract_excerpt":"A 1-ended finitely presented group has semistable fundamental group at $\\infty$ if it acts geometrically on some (equivalently any) simply connected and locally finite complex $X$ with the property that any two proper rays in $X$ are properly homotopic. If $G$ has semistable fundamental group at $\\infty$ then one can unambiguously define the fundamental group at $\\infty$ for $G$. The problem, asking if all finitely presented groups have semistable fundamental group at $\\infty$ has been studied for over 40 years. If $G$ is an ascending HNN extension of a finitely presented group then indeed, $G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09140","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"}