{"paper":{"title":"The pseudo-Anosov and conjugacy problems are in $\\textbf{NP} \\cap \\textbf{co-NP}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Mark C. Bell","submitted_at":"2014-10-06T12:54:17Z","abstract_excerpt":"For a fixed marked surface $S$, we construct polynomial bounds on the periodic and preperiodic lengths of the maximal splitting sequences of a projectively invariant measured train track.\n  We give two consequences of these bounds. Firstly, that the problem of deciding whether a mapping class is pseudo-Anosov lies in $\\textbf{NP}$. This is dual to the previously known result that the pseudo-Anosov problem is in $\\textbf{co-NP}$. Secondly, that the problem of deciding whether two mapping classes are conjugate lies in $\\textbf{co-NP}$. Similarly, this is the dual to the previously known result t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1358","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"}