{"paper":{"title":"Cannon-Thurston maps for hyperbolic free group extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Kapovich, Samuel J. Taylor, Spencer Dowdall","submitted_at":"2015-06-23T12:51:18Z","abstract_excerpt":"This paper gives a detailed analysis of the Cannon--Thurston maps associated to a general class of hyperbolic free group extensions. Let $F_N$ denote a free groups of finite rank $N\\ge 3$ and consider a \\emph{convex cocompact} subgroup $\\Gamma\\le Out(F_N)$, i.e. one for which the orbit map from $\\Gamma$ into the free factor complex of $F_N$ is a quasi-isometric embedding. The subgroup $\\Gamma$ determines an extension $E_\\Gamma$ of $F_N$, and the main theorem of Dowdall--Taylor \\cite{DT1} states that in this situation $E_\\Gamma$ is hyperbolic if and only if $\\Gamma$ is purely atoroidal.\n  Here,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06974","kind":"arxiv","version":3},"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"}