{"paper":{"title":"Applications of weak attraction theory in Out($F_n$)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Pritam Ghosh","submitted_at":"2013-06-25T18:05:25Z","abstract_excerpt":"Given a free group of rank r >= 3 and two exponentially growing outer automorphisms {\\psi} and {\\phi} with dual lamination pairs {\\Lambda^\\pm}_{\\psi} and {\\Lambda^\\pm}_{\\phi} associated to them, which satisfy a notion of independence described in this paper, we will use the pingpong techniques developed in recent works of Handel and Mosher to show that there exists an integer M > 0, such that for every m, n >= M, {\\psi}^m and {\\phi}^n will freely generate a group of rank two and every element of this free group which is not conjugate to a power of the generators will be fully irreducible and h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6049","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"}