{"paper":{"title":"Subgroup decomposition in $\\text{Out}(F_n)$, Part III: Weak attraction theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Lee Mosher, Michael Handel","submitted_at":"2013-06-19T22:31:43Z","abstract_excerpt":"This is the third in a series of four papers (with research announcement posted on this arXiv) that develop a decomposition theory for subgroups of $\\text{Out}(F_n)$.\n  In this paper, given an outer automorphism of $F_n$ and an attracting-repelling lamination pair, we study which lines and conjugacy classes in $F_n$ are weakly attracted to that lamination pair under forward and backward iteration respectively. For conjugacy classes, we prove Theorem F from the research annoucement, which exhibits a unique vertex group system called the \"nonattracting subgroup system\" having the property that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4712","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"}