{"paper":{"title":"Detecting fully irreducible automorphisms: a polynomial time algorithm. With an appendix by Mark C. Bell","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Kapovich","submitted_at":"2016-09-13T13:21:23Z","abstract_excerpt":"In \\cite{Ka14} we produced an algorithm for deciding whether or not an element $\\phi\\in Out(F_N)$ is an iwip (\"fully irreducible\") automorphism. At several points that algorithm was rather inefficient as it involved some general enumeration procedures as well as running several abstract processes in parallel. In this paper we refine the algorithm from \\cite{Ka14} by eliminating these inefficient features, and also by eliminating any use of mapping class groups algorithms.\n  Our main result is to produce, for any fixed $N\\ge 3$, an algorithm which, given a topological representative $f$ of an e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03820","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"}