{"paper":{"title":"When is a polynomially growing automorphism of $F_n$ geometric ?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Kaidi Ye","submitted_at":"2016-05-24T11:50:39Z","abstract_excerpt":"The main result of this paper is an algorithmic answer to the question raised in the title, up to replacing the given $\\hat{\\phi} \\in Out(F_n)$ by a positive power.\n  In order to provide this algorithm, it is shown that every polynomially growing automorphism $\\hat \\phi$ can be represented by an iterated Dehn twist on some graph-of-groups $\\cal{G}$ with $\\pi_1{\\cal{G}} = F_n$. One then uses results of two previous papers \\cite{KY01, KY02} as well as some classical results such as the Whitehead algorithm to prove the claim."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07390","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"}