{"paper":{"title":"An effective algebraic detection of the Nielsen--Thurston classification of mapping classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Johanna Mangahas, Thomas Koberda","submitted_at":"2013-12-20T21:19:30Z","abstract_excerpt":"In this article, we propose two algorithms for determining the Nielsen-Thurston classification of a mapping class $\\psi$ on a surface $S$. We start with a finite generating set $X$ for the mapping class group and a word $\\psi$ in $\\langle X \\rangle$. We show that if $\\psi$ represents a reducible mapping class in $\\Mod(S)$ then $\\psi$ admits a canonical reduction system whose total length is exponential in the word length of $\\psi$. We use this fact to find the canonical reduction system of $\\psi$. We also prove an effective conjugacy separability result for $\\pi_1(S)$ which allows us to lift t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6141","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"}