{"paper":{"title":"Deciding reducibility of mapping classes is in $\\textbf{NP}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Mark C. Bell","submitted_at":"2014-03-12T16:05:55Z","abstract_excerpt":"For a fixed marked surface $S$, we show that the problem of deciding whether or not a mapping class is reducible lies in $\\textbf{NP}$. As usual this immediately gives an exponential time algorithm to decide whether or not a mapping class is reducible.\n  To do this we use an (ideal) triangulation to obtain a coordinate system on the set of multicurves on $S$. The result then follows from the fact that the action of the mapping class group of $S$ is piecewise-linear with respect to such a coordinate system and so we are able so show that: if a mapping class $h$ fixes a multicurve then it fixes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2997","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"}